







A hexagon constructed from two triangles 
20200413 

From sunny: Triangles AEC and FDB are equilateral triangles and EA= DF= 12cm. The polygon
at the center of the star is a regular hexagon. What is the area of the hexagon? Answered by Penny Nom. 





A congruence theorem for two right angled triangles 
20160717 

From Sayari: Hello.
Is it possible for two right angled triangles to have the same length of base and height and a different hypotenuse? If not so, then why in the congruence criteria RHS the hypotenuse is given more importance? It can also be like 'two triangles are congruent if they are right angled and have the same base and height.'
Thank You. Answered by Penny Nom. 





A trough with a triangular cross section 
20160521 

From Clarice: A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough? Answered by Penny Nom. 





The angles of a triangle 
20151217 

From Faith: Does the measure of angle determine the length of its side? For example two angles are congruent then the sides are also congruent because from my understanding the angle determine the shape of triangle. Answered by Penny Nom. 





The length of a shadow 
20150801 

From maaz: Hello
I am having trouble with this question:
Lizzie, who is 6 feet tall, stands in her driveway at night, exactly
24 feet from the base of a spotlight, and casts a shadow that is 12
feet long if her friend Hannah who is 5 feet tall decides to stand
next to lizzie how long will her shadow be? Answered by Penny Nom. 





A barge of triangular cross section 
20140818 

From tushar: a barge of triangular cross section is 20m long 12 m wide and 6m deep.its floats in SW at a draft if 4m find its displacement Answered by Penny Nom. 





The length of a shadow 
20140509 

From vijay: A girl of height 80 cm is running away from the base of a lamppost at a speed of 2 m/s. If the lamp is 4 m above the ground, find the length of her shadow after 5 seconds. Answered by Penny Nom. 





Two cones 
20140409 

From c.j: what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Answered by Penny Nom. 





Shadows of a father and son 
20140402 

From esada: the father and son cast a shadow of 11 feet and 8 feet,respectively if the son is 4'8'' in height,how tall is the father? Answered by Penny Nom. 





A triangle construction 
20130727 

From Nazrul: Two angles and the difference of the lengths of their opposite sides of a
triangle are given. How can I draw the triangle.
Please help me. Answered by Chris Fisher. 





A triangle and an incircle 
20130509 

From Max: On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line.
The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this. Answered by Chris Fisher. 





Three right triangles 
20120726 

From Jora: I am having a lot of difficulties with this question.
Name: Jora
Subject: Math
Who are you: Student Answered by Chris Fisher. 





Squares and triangles 
20111206 

From Liaqath: You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have? Answered by Penny Nom. 





Dividing a polygon into triangles 
20110416 

From Foxie: You have a given regular polygon with n vertices and you divide it into triangles(using the vertices of the polygon) which each share at least one side with the polygon. How many distinct ways can you divide the polygon if its vertices are numbered? For n=3 it's 1 way, for n=4 it's 2 ways for n=5 5 ways, I'm not quite sure but think that for n=6 it's 12 ways... thanks in advance! Answered by Claude Tardif. 





Triangles with perimeter 16 cm 
20110222 

From Chong: How many triangles (up yo congruence) with perimeter 16 cm and whose lengths of its side are integers? Answered by Chris Fisher. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





The height of a lamp 
20110113 

From Dorothy: I need to find the lamp height with casting shadow (base line of triangle where a boy 1.6m tall stands 3m from base of street lamp and has a 2m shadow. In other words, think of a right angle triangle with zero height starting at left, then 2m to right stands boy (1.6m high). Angle (hypotenuse) increases up to top of street lamp with 'x' height and 3m base. Answered by Penny Nom. 





Draw a figure with 16 triangles using only 6 line segements 
20101216 

From Jill: How can you draw a figure with 16 triangles using only 6 line segements? Answered by Stephen La Rocque. 





How many triangles...? 
20100222 

From deciree: Given 12 points, no 3 of them on a line with 6 red, 4 blue and 2 green points.
a) How many triangles have vertices all the same color?
b)How many triangles have vertices with each vertex a different color?
c)How many triangles have at least one green vertex?
thanks to lorraine! Answered by Penny Nom. 





Triangles 
20100219 

From Wiliam: A box contains one 2 inch rod, one 3 inch rod, one 4 inch, and one 5 inch rod.
What is the maximum number of different triangles that can be made using these rods as sides? Answered by Penny Nom. 





Triangles on a base of 2.4 meters 
20091226 

From Allan: Please,How do I calculate the height of a triangle when I only know the width of the base line,It is 2.4 mtrs. Thankyou very much. Answered by Penny Nom. 





The line through D(4, 0) and E(2, 6) 
20091116 

From Rogerson: The point F is on the line through D(4, 0) and E(2, 6) so that DF=4DE. Find the coordinates of F. Answered by Penny Nom. 





A paper towel roll 
20090819 

From Jeff: I am making a spiral tube with paper that is 2" in dia. and 102" long
I will be using paper that is slit 3" wide how many lineal feet of paper will
I need to to cover the 102"
I will be using 3 rolls of paper that will over lap the other by half to make
a hard tube (paper core) in a roll of paper towels
Thanks Jeff Answered by Penny Nom. 





The position of the fulcrum 
20090523 

From jim: I think I need a formula. I need to know how far an object will be lifted.
A beam is 246 inches long on one side of the fulcrum, and 41 inches on the other side,
if I push down 36 inches on the long side of the beam, how much will the short side move up? Answered by Stephen La Rocque. 





Triangles within triangles 
20090224 

From Mari: a large shaded triangle changes each day with a white triangle appearing
in the center of each shaded one. If this pattern continues, how many white
triangles will be there on the 6th day? On the 6th day, what fraction of
the large outer triangle will be white?THANKS! Answered by Robert Dawson. 





Trig functions without geometric data 
20090224 

From bob: I do not understand how it is possible to find the sine, cosine, or tangent of an angle if
there is no hypotenuse, opposite or adjacent side?! Answered by Robert Dawson. 





A 306090 triangle 
20090203 

From Inez: If you have a 306090 triangle and the only side you get is 73 and a 90 degree box, how do you find the area? Answered by Penny Nom. 





The volume of a feed hopper 
20081218 

From John: I need to calculate the volume of a feed hopper, and I'm not sure how to break it down. The top of the hopper is 36" x 36", it is 30" deep, and ends at a 6" x 6" plate. One side of the hopper is straight top to bottom, of course tapering on two sides to meet at the plate. The other three sides angle down at about 75 degrees. I need to determine the cubic foot volume of this hopper (it is used for ground coffee) so I can configure a vibrator to knock down residual grounds. Thanks. Answered by Robert Dawson. 





3 equidistant points 
20081201 

From Damien: How do you find 3 equidistant points (C,D,E) on a line between point A(Xa, Ya) and point B(Xb, Yb) so that AC, CD, DE and EB are all equal? Answered by Chris Fisher. 





The midpoint o a line segment 
20081115 

From Jane: The vertices of a triangle are at (1,7), (6,1) and (0,3). Find the coordinates of the midpoints of the sides. Answered by Penny Nom. 





The angles and sides of a triangle 
20081113 

From JAMIE: a triangle with a side(b)37m an angle(C)70degrees and (a)79m find values of angles A and B and length of side c Answered by Stephen La Rocque. 





A flagpole and a yardstick 
20081107 

From Wanda: One boy holds a yardstick vertically at a point 40 feet from the base of the flagpole. The other boy backs away from the pole to a point where he sights the top of the pole over the top of the yardstick. If his position is 1 ft 9 in from the yardstick and his eye level is 2 ft above the ground, find the height of the flagpole. Answered by Penny Nom. 





Joining vertices in a polygon 
20080818 

From Megan: I'm trying to develop a relationship between the number of points of a regular polygon and the
(a) number of lines you could draw between those points,
(b) number of triangles you could draw,
(c) number of quadrilaterals,
etc. Answered by Penny Nom. 





Similar Triangles Given a Median 
20080817 

From RAM: Sides AB , AC and median AD of a triangle ABC are respectively proportional to
PQ PR and median PM of another triangle PQR. Show that ABC is similar to PQR Answered by Janice Cotcher. 





Similar triangles 
20080812 

From ramarao: D is a point on side BC of a triangle ABC such that BD/CD=AB/AC. prove that AD is the bisector
AD is the bisector of BAC Answered by Chris Fisher. 





The Pythagorean theorem with triangles rather than squares 
20080429 

From Zachary: I need to figure out how to prove the pythagorean theoorem using equilateral triangles
instead of using square. I know that A^2+B^2=C^2, but how do you get that by using equilateral
triangles. I know the area of a triangle is BH1/2=Area. So what i need to know is how to derieve the
formula of a triangle to get the pythagorean theorem Answered by Penny Nom. 





Similar triangles 
20080326 

From Nisha: In triangle ABC, LM is parallel to AB. If AL=x3,AC=2x,BM=x2,BC=2x=3. Find x Answered by Penny Nom. 





A 6 pointed star 
20080304 

From Siddharth: When 2 congruent equilateral triangles share a common center, their union can be a star
If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles?
a) 60 b) 70 c) 80 d)90 e)100 Answered by Stephen La Rocque. 





Two right triangles 
20080218 

From Amy: Hi, I have a problem that has me stumped.
There are two right triangles that share the same adjacent side (AB) which
is 240'. The right angles of each triangle are at the opposite ends of the
shared side.
The Opposite side (AC) of Triangle ABC is 180'
and the Hypotenuse (CB) is 300'.
The Opposite side (BD) of Triangle ABD is 100'
and the Hypotenuse (AD) is 260'.
How do I figure out where the hypotenuses intersect? Answered by Stephen La Rocque and Harley Weston. 





A flagpole and a statue 
20080209 

From Krista: A flagpole casts a ten meter (m) shadow at the same time as a six metre (m) statute beside it casts a two metre shadow. What is the height of the flagpole?? Answered by Steve La Rocque and Penny Nom. 





Forces on an inclined plane 
20080110 

From Ron: A body that weighs 540lbs is caused to slide up an inclined plane with a uniform velocity by a force that acts parallel to the plane. For each foot of horizontal distance, there is a vertical rise of 2in. If the coefficient of sliding friction is 0.16, what force is required to move the body? Answered by Stephen La Rocque. 





Lining up coins visually using geometry and trigonometry 
20071231 

From Jessica: a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a halfdollar so that they all have the same apparent size? The diameters of the coins, in thousandths of inches, are as follows: penny, 750; nickel, 835; dime, 705; quarter, 955; halfdollar, 1205.
b) How should the coins be placed, if the distance between the dime and the halfdollar is 100 units?
How far from thw dime should your eye be to see that all the coins have the same apparent size?
c) What angle do the coins subtend when they have the same apparent size? Answered by Stephen La Rocque. 





How many triangles can be formed? 
20071221 

From pankaj: Q.There is 2 lines parallel to each other. If 1st has 5 points in it and 2nd 3 points in it,how many triangles can be formed? Answered by Penny Nom. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





Related Rates (streetlamp and shadow) 
20071109 

From Casey: A street light is mounted at the top of a 15ft pole. A man 6ft tall walks away from the pole at a rate of 5ft per second. How fast is the tip of his shadow moving when he is 40ft from the pole? Answered by Stephen La Rocque and Penny Nom. 





Two triangles 
20071108 

From Barbara: If the base of a larger triangle is 34 inches long, what is the length of side A of the smaller triangle?
(the small triangle has on top the letter a on the right side of the triangle it has the letter b, and at the bottom of the small triangle it has the number 17) Answered by Penny Nom. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





Similar triangles 
20070829 

From James: Question: In the triangle ABC, X is a point on AC. AX = 15 m and XC = 5 m. The angle AXB is 60 degrees and the angle ABC is 120 degrees. Find the length of BC.
I am sure to an extent that this has to do with similar triangles, but I am not certain. Answered by Harley Weston. 





Finding the radius of an inscribed circle 
20070705 

From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher. 





Volume in a triangular water trough 
20070624 

From David: A water trough has sloping sides of length 500mm making it triangular in cross section, with vertical ends. The width at the top is 600mm and the length is 2.0 metres.
(i) Calculate the capacity of the trough, giving your answer accurate to the nearest litre.
(ii) Find out the depth of the water when the trough is half full. Answered by Stephen La Rocque. 





Similar triangles 
20070221 

From Vivienne: The lengths of the sides of a triangle are 8, 15, & 17. If the longest side of a simlar triangle is 51, what is the length of the shortest side? Answered by Stephen La Rocque and Penny Nom. 





Height of a right triangle? 
20070129 

From Engelbert: The base of the right triangle is 50 ft. At the angle (on the base of the triangle) across from the right angle is labeled portion (a triangle within a triangle), the base of this little triangle is 10 ft. and the height is 6 ft. What equation can i use to solve this? Answered by Steve La Rocque and Haley Ess. 





In the shadow of a building 
20070111 

From Bill: if a building b feet cast a shadow f feet long, then, at the same time of the day, a tree t feet high will cast a shadow, how many feet long? Answered by Stephen La Rocque. 





How do the perimeters of the two pentagons compare? 
20070102 

From Robert: If the area of one pentagon is eightyone times the area of another pentagon, how do the perimeters of the two pentagons compare? Answered by Penny Nom. 





The height of a building 
20061119 

From Sweetie: I have to figure out the measure of the water towers antenna on my schools campus using up to two items created by me and a manual. I don't know far away we are going to have to be. I need to have a fool proof way to figure out the distance to the tower. I have an idea using trigonometry but its really roughly estimated. Do you have any suggestions? Answered by Stephen La Rocque. 





An equilateral triangle has been wedged in between two circles. 
20060922 

From Kim:
An equilateral triangle has been wedged in between two circles. How does the diameter of the smaller circle compare to the diameter of the larger circle.
image: circle inside of an equilateral triangle touching all sides of the triangle; both the triangle and the circle inside are placed into a larger circle where the triangle vertices all touch the circle
Answered by Penny Nom. 





The length of 2 sides of a triangle 
20060915 

From Lonnie: I need to know how to figure the length of 2 sides of a triangle, as the following example:
The length of the bottom is 12' and the angles are 45, 45 I need to know how long the other 2 sides must be to get an angle of 90 at the top. Answered by Stephen La Rocque. 





How fast is the water level rising 
20060812 

From Erin: Water runs into a conical tank at the rate of 9ft^{3}/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r^{2} h). Answered by Penny Nom. 





Designing a garage 
20060608 

From A builder: I'm currently designing a garage and came upon this interesting math problem. I've tried using various methods to solve it but have so far been unsuccessful. I've included a picture as its far easier to show you my question than explain it verbally. I realize it could be done by trial and error but i'm looking for a real solution. Answered by Stephen La Rocque and Penny Nom. 





The volume of water in a cone 
20060321 

From Ghulam: A vessel has the shape of an inverted cone.The radius of the top is 8 cm and the height is 20 cm. Water is poured in to a height of x cm.Show that if the volume of the water is V cubic cm,then V=(4/75)pi x3. Answered by Penny Nom. 





Heights and shadows 
20060306 

From Debra: A person is 7 ft tall and his shadow is 10 ft tall. using the same info what is the shadow of a person who is 5ft tall
Answered by Stephen La Rocque. 





How do you find the angles in a triangle? 
20060127 

From Keith: How do you find the angles in a triangle if you know the lengths of the sides? Answered by Chris Fisher and Penny Nom. 





Subdividing a polygon into triangles 
20060126 

From Adam: is there an algorithm to divide a regular polygon into N
equilateral triangles having the same area (no limit on N), or if not, an
algorithm to divide a regular polygon into N triangles having the same shape
and size? Answered by Chris Fisher. 





The third side of a triangle 
20060125 

From Bob: Is there any way to obtain the third side of a triangle when 2 sides are the same length (2.18 inches). I also need to find the angles. Answered by Penny Nom. 





Triangles with integer sides 
20051104 

From Tammy: I am trying to find another pair of integer sided isosceles triangles, not the same as the ones listed below, with equal areas.
(5,5,8)
(5,5,6) Answered by Chri Fisher. 





A 306090 triangle 
20050911 

From Gary: I have the length of only 1 side of triangle with angles of 306090 degrees. How can I find the length of the other 2 sides? Answered by Penny Nom. 





The centroid of a triangle 
20050407 

From Maria: Q3)find the coordinates of the centroid of triangle ABC
i want your help here to solve the 3rd question i got stuck. Answered by Penny Nom. 





Solving triangles 
20041030 

From Allen: Solve the following triangles.
Given
1. B = 20 Degrees, a = 25, b = 16
2. A = 35 Degrees, b = 2, c = 3
3. A = 32 Degrees, C = 44, c = 20 Answered by Harley Weston. 





Water in a cone 
20040728 

From A student: A vertically inverted cone( i.e. vertex down) has a radius 7
inches and height 24 inches. Water is filled to one third of its
height .Find the ht of water when cone is turned upside down Answered by Penny Nom. 





A Fibonacci triangle 
20040425 

From Marcelle: Is it possible to construct a triangle with sides that are three consecutive Fibonacci numbers? Answered by Walter Whiteley. 





The sum of angles in a triangle 
20040406 

From A student: How can u prove sum of angles in a triangle equal to 180 degrees? Answered by Penny Nom. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





Napoleon's theorem 
20040227 

From David: How do i prove this : For any triangle, if you make 3 equillateral triangles
using the sides of the the original triangle, the central points of the 3
tringles another triangle that is equillateral.z Answered by Chris Fisher and Penny Nom. 





The area of a triangle 
20031201 

From A student: Find the Area of Triangle ABC
A(3,2)
B(4,0)
C(0,8) Answered by Penny Nom. 





Two chords 
20031007 

From Lori: Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Answered by Penny Nom. 





Water in a cone 
20030812 

From Adrienne:
Water is poured into a tank in the shape of an inverted right circular cone.ð The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.ð (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Answered by Penny Nom. 





An equilateral triangle 
20030317 

From Shirley: An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. How many of these triangles are possible? Answered by Penny Nom. 





The area of an isoceles triangle 
20030207 

From A student: I have to find the area of an isoceles triangle with one angle side of 30 degrees, and length of base 5. Could you please help me solve this problem? Answered by Penny Nom. 





A Circle is evenly divided into six equal triangles 
20020916 

From Marilynn: A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Answered by Paul Betts. 





The area of a triangle 
20020907 

From Phill: How do you find the area of a equilateral and other triangles? Answered by Penny Nom. 





Find the angle measures 
20020518 

From Amanda: In triangle ABC; the measure of angle A is 20 degrees more than twice the angle B. The measure of angle C Is five times angle B. Find the angle measures. Answered by Penny Nom. 





Two triangles 
20020403 

From Scott: Consider 2 triangles: Triangle PMB and Triangle PLA. Triangle PLA is contained within Triangle PMB. Side LA is parallel to Side MB. Point L is located on Side PM. Point A is located on Side PB. If the ratio PL:LM = 5, then what is PB:PA ?? Answered by harley Weston. 





Similar triangles 
20010908 

From Dave: I am standing on the bank of a river ( whose banks are parallel here) directly opposite a boathouse, B, on the opposite bank. I walk along the bank of the river past a signpost, S, until I reach a point C distant 60 metres from where I started walking. I then walk away from the bank, at right angles to the bank, until I reach a shady tree at D. Attached to teh tree is a sign stating that this spot is 45 metres from the signpost. C is 36 metres beyond S and B and S are in line from D. (a) How far did I walk away from the bank of the river?? (b) Calculate the width of the river? Answered by Penny Nom. 





An inequality involving triangles 
20010612 

From Sandra: The triangle inequality guarantees that the sum of the lengths of two sides of a triangle is greater than the length of the third. As a consequence, if x and y are legs of a right triangle, with x less than or equal to y, and z the hypotenuse, then x + y is greater than z, so x is greater than z  y. Under what circumstances will x is greater than 2(z  y) be true? Answered by Chris Fisher and Penny Nom. 





Geometry problems involving triangles 
20010607 

From Sandi: Find the radius of the largest circle contained in a right triangle whose legs are 8 and 15 and hypotenuse is 17. If the right triangle has legs a and b and hypotenuse c, find an expression for the radius of the circle. Answered by Penny Nom. 





The angles in a triangle 
20010511 

From Nikki: Find the measure, to the nearest degree, of each angle of a triangle with sides of the given lengths. 26, 35, 40 Answered by Penny Nom. 





Triangles and fractions 
20010427 

From Constance: My name is Constance and I am thirteen years old (I am a student). The question that I am queering about I don't understand why you do ONE HALF x the base x the width WHEN YOU WANT TO FIND the area of a triangle? My second question is if you multiply one half and 10 together why does it come out as 5? Answered by Penny Nom. 





How tall is the tree? 
20010302 

From Ronda: a tree's shadow is 42 ft. long. There is a stop sign that is right next to it and it is 18 ft. tall and it's shadow is 12 ft. long. How tall is the tree? Answered by Penny Nom. 





A lampost and its shadow 
20001224 

From Laura: A lamppost line EC casts a shadow line AC. A 30 cm ruler line DB has been moved from A so that it's shadow falls just within the shadow of the lamppost.  Suppose the length of the ruler's shadow is 42 cm. What is the slope of the imaginary line AE?
 Suppose the lamppost's shadow is 15 m. long. How tall is the lamppost?
Answered by Penny Nom. 





Is this a right triangle? 
20001208 

From Alicia: How would you setup and answer a problem like these one? Triangle ABC has vertices A(2,2), B(1,2), and C (1,2). Use slopes to determine if the triangle is a right triangle. Answered by Penny Nom. 





Triangles and trigonometry 
20001130 

From Mose: If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Answered by Harley Weston. 





Length of a shadow 
20001101 

From Jessy: A man who is six feet tall is walking away from a street light that is fifteen feet tall. How long is the man's shadow when he is ten feet away from the light? Answered by Penny Nom. 





A centroid problem 
20000602 

From Kerstin: An isoceles triangle has sides measuring 13 cm, 13 cm, and 10 cm. Find the distance from the centroid to the vertex of a base angle. Answered by Harley Weston. 





The side length ratios of some triangles 
20000404 

From Alexis Lockwood: I am doing a project for my Math 30B class regarding the side length ratios of 454590 degree and 306090 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter. Answered by Harley Weston. 





Area of a quadrilateral 
19991119 

From Zane Cram: I need the formula to calculate the area of an irregular sided rectangle. Each side has a different measurement or length. Answered by Walter Whiteley. 





Isosceles triangles 
19991012 

From Amber: In defining the types of triangles, our class was stumped by a question asked by one of the student. Maybe you could help. The definition of an equilateral triangle is a triangle with three congruent sides. The definiton of an isosceles triangle is a triangle with at LEAST two congruent sides. The question is, if an isosceles triangle only requires at Least two of the sides to be congruent, could an equilateral triangle be called an isosceles triangle? Answered by Penny Nom, Walter Whiteley and Chris Fisher. 





Two 12sided polygons 
19990925 

From Kelly Boulton: Two 12sided polygons are similar. A side of the larger polygon is 3 times as long as the corresponding side of the smaller polygon. wHAT IS the ratio of the area of the larger polygon to the area of the smaller polygon. Answered by Walter Whiteley. 





Degrees and triangles 
19990909 

From Sandra Mills: Are there any triangles which are not 180 degrees? I am also in need of information on the history of degree measure for an angle. Answered by Walter Whiteley. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Shimin's Geometry Problem 
19971202 

From Ong Shimin: ABCD is a rectangle. X and Y are the midpoints of BC and CD respectively. W is a point on AB such that AW : WB = 2 : 1. Z is a point on AD such that AZ : ZD = 2 : 1. WY intersects XZ at O. If the area of triangle WOZ is 84 centimeters squared, find the area of triangle XOY. Answered by Chris Fisher. 





Triangles, The Pythagorean Theorem and Pizzas. 
19970223 

From Sherryle Mathis: I am a graduating senior presently teaching geometry as part of my student teaching. I will do my CUP on Right Triangles and Pythagorean theorem. I am looking for a fun activity as part of my unit plan. Answered by Walter Whiteley. 





Un polyedre ayant comme face 20 triangles 
20000802 

From Sonia: J'aimerai savoir comment s'appelle un polyedre ayant comme face 20 triangles équilatéraux égaux. Answered by Chris Fisher. 





Maths 
19990111 

From Stephane Roissard: Soit ABC un triangle dans lequel les trois médianes sont de meme longueur. Montrer que ce triangle est quilatéral. Answered by Jack LeSage. 





Question de trigonométrie 
19971211 

From JeanPierre Quesnel: Je suis dans le désert et je parcours 1000 km à partir du point "A" jusqu'au point "B". Si je reviens au point "A" et fais une rotation de 8 degrés en faisant un autre 1000 km, quelle sera la distance en km entre les points "B" et "C". Answered by Diane Hanson et Penny Nom. 

