







An equilateral triangle 
20190410 

From ethan: In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0). Find the coordinates of S in terms of a. Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20190129 

From Penny: What is the length of each side of the largest equilateral triangle that fits inside a 3 inch diameter circle? Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20170915 

From sumit: what is the area (in sq. unit) of an equilateral triangle inscribed in the circle x^2+y^24x6y23=0. Answered by Penny Nom. 





A circle inscribed in an equilateral triangle 
20161127 

From jo: what is the radius of the inscribed circle of an equilateral triangle with altitude 12 units? Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20150611 

From Casey: I have an equilateral triangle inscribed in a circle  this triangle
has been bisected to give me 2 right triangles. I know the length
of the line bisecting the equilateral triangle is 36 inches. How do
I figure out the circumference of the circle and the length of the
sides of the equilateral triangle? Answered by Penny Nom. 





The height of an equilateral triangle 
20150312 

From anna: I am anna and i am in 7th grade.
i am trying to find the height of and equilateral triangle, all sides equaling 4 inches Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20130117 

From Nicole: How do you find the shaded region of a circle if an unshaded equilateral triangle in inscribed in it. The only other things I know about the problem are that the side lengths of the equilateral triangle are 14 inches. Answered by Penny Nom. 





The perimeter of an equilateral triangle 
20121214 

From shreyaarora: if the area of on equilateral triangle is 24/3cm,then what is its perimeter Answered by Penny Nom. 





An equilateral triangle and a regular hexagon in a circle 
20120911 

From Heidemarie: The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle. Answered by Penny Nom. 





A circle drawn around a equilateral triangle 
20120401 

From BIMAL: what is the diameter of a circle drawn around a equilateral triangle of size 6 cm Answered by Penny Nom. 





Gravel, sand, cement and an equilateral triangle 
20120321 

From saheed: how many tonnes of gravel and sand,bags of cements will be required to concrete 5feet depth/deep of 4feet equilateral triangle? Answered by Harley Weston. 





The height of an equilateral triangle 
20120229 

From Carley: Hi my name is Carley. I am an 8th garder. What us the height of an equilateral triangle si the sides are 18 cm? Answered by Penny Nom. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





The sides of an equilateral triangle 
20110127 

From Cristal: Hello :) How can i find the sides of an equilateral triangle when only given the height 10m? Answered by Penny Nom. 





Can determine if it is scalene, isosceles, or equilateral 
20101201 

From Jessie: find the measures of the sides of triangle KPL and classify each triangle by its sides. my first problem would be K(3,2) P(2,1) L(2,3) ...The three points they give you are the vertices of the triangle and you need to match them up. Draw the triangle and write in the vertices and the related point with the vertex. You will then do the distance formula three times to find the distance of all three sides. Once you have the three sides you can determine if it is scalene, isosceles, or equilateral...using the distance formula how do i solve this? Answered by Penny Nom. 





The area of an equilateral triangle 
20101111 

From ginny: If a equilateral triangle has side lengths of 41.33m how would i calculate the area?
if i don't know the height of the triangle?
thank you. Answered by Penny Nom. 





The vertices of an equilateral triangle 
20100219 

From Emma: If two of the vertices of an equilateral triangle are (2,1) and (6,5), what
are the two possible coordinates of the third side of the triangle? Answer
in radical form. Answered by Tyler Wood. 





Solve for s 
20090812 

From Michelle: My daughter and I are having trouble with this problem...All it says i solve thr formula for the indicated variable.
Height of an Equilateral Triangle.
Solve for s:
H= square root of 3/2 * S Answered by Penny Nom. 





An equilateral triangle 
20081217 

From lorraine: an equilateral triangle has side lenghts of10.the length of its altitude is? Answered by Penny. 





The height of an equilateral triangle 
20081106 

From touqeer: My question is that how can we find the height of an equilateral triangle without using pythagoras theorem? Answered by Penny Nom. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





The perimeter of an equilateral triangle 
20080911 

From Gerry: How can I find the perimeter (length of side) of an equilateral triangle if the only information I have is the altitude? Answered by Penny Nom. 





An equilateral triangle 
20080721 

From Meagan: An equilateral triangle has vertices at (0,0) and (6,0) in a coordinate plane. What are the coordinates of the third vertex? You may want to sketch it out.
Note: The sides of an equilateral triangle are identical in length. Answered by Harley Weston. 





Two triangles and a circle 
20080703 

From Anita: An equilateral triangle with side of length 1 cm is inscribed in a circle. A second equilateral triangle is circumscribed about the circle with all sides tangent to the circle. Find the length of a side of the second triangle. Answered by Harley Weston. 





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. 





The area of an equilateral triangle 
20080328 

From ElizabethMorgan: I have a problem that reads:
Find the area of a triangle with sides of 4 cm. Find the height first.
This means that I have an equilateral triangle, and I need a formula
to calculate the height using the base, and the sides. Answered by Stephen La Rocque. 





The area of an equilateral triangle 
20080316 

From michael: my daughter has been given a task and I'm stuck too.
if an area of an equilateral triangle = 85cm squared
there are no other dimensions provided.
how do I calculate the length of each side ? please 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. 





A proof in geometry 
20080227 

From Kimberly: I'm trying to write a proof for the following: If all altitudes are equal in an equilateral triangle then all sides are equal. Answered by Stephen La Rocque and Penny Nom. 





Finding all the angles 
20071213 

From Rajesh: An eqilateral triangle is drawn in a square with one of the side as its base and draw the lines from the other angular sides such that there are four triangles
formed inside the square which includes the equilateral triangle.I want to know all the angles of all the triangles formed inside the square. Answered by Stephen La Rocque and Penny Nom. 





The length of the side of a triangle 
20071028 

From devon: hay ok i have the height of a triangle but how do i find the length od the side if all of the sides are the same length Answered by Penny Nom. 





An equalateral triangle is 30 acres 
20071028 

From mike: If the area of an equilateral triangle is 30 acres, what is the length of each side in feet or miles? Answered by Penny Nom and Victoria West. 





An equilateral triangle with height 2 inches 
20071023 

From Christine: I'm doing an project in school about tessellations.
But first, I have to construct an equilateral triangle with an altitude of exactly 2 inches.
I know how to draw an equilateral triangle...but I don't know what I have to do in order for the triangle to have an altitude of 2 inches. Answered by Penny Nom. 





The area of equilateral triangle 
20070605 

From solomon: describe the area of equilateral triangle in terms of its side? solve in two ways. Answered by Stephen La Rocque. 





Area of an equilateral triangle 
20070509 

From Diana: how do i find the area of an equilateral triangle when they give us the base? Answered by Penny Nom. 





Can the triangle be called both an acute triangle and an equilateral triangle? 
20070310 

From Jane: If all sides of a triangle are the same length and all angles are 60 degrees, can the triangle be called both an acute triangle and an equilateral triangle? Answered by Walter Whiteley. 





Can an equilateral triangle have an obtuse angle? 
20060326 

From Chris: Can an equilateral triangle have an obtuse angle?
I'm thinking not, because all sides must be equal, but
does that also imply that all angles are equal?
Answered by Stephen La Rocque. 





Three towns are located at the vertices of an equilateral triangle 
20060320 

From A student: three towns are located at the vertices of an equilateral triangle. The towns are 8, 5, and 3 miles, respectively, from a store. How far apart are the towns? Answered by Chris Fisher. 





An equilateral triangle and a regular hexagon 
20060228 

From Trevor: An equilateral triangle and a regular hexagon have equal length perimeters. What is the ratio of their areas? Answered by Penny Nom and Stephen La Rocque. 





Constructing figures 
20050920 

From Kim: I would like to know how to draw different shapes:
Regular Octagon with sides of length, 1 unit
Equilateral Triangles, with sides of length 1 unit
Regular Hexagons, with sides of length 1 unit
Isoseles Triangles, with hypotenuse of length 1 unit
Answered by Penny Nom. 





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. 





Area of an equilateral triangle 
20031125 

From Jared: Can you help me understand why the area of a equilateral triangle is the square root of 3 divided by 4 times the lenght of the side squared? Answered by Penny Nom. 





The height of an equilateral triangle 
20030406 

From Rosa: If Each side of an equilateral triangle is 10 m. What is the height? 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. 





An equalateral polygon inscribed within an ellipse 
20020630 

From Steven: How would you calculate the length of one of the sides of an equalateral polygon (of n sides) inscribed within an ellipse ( of any eccentricity ) where all of the vertices exactly touch the perimeter of the ellipse? I know that when the eccentricity is zero ( i.e a circle ) the formula: r * (sin(180/n) * 2) will suffice. But what about when the eccentricity is greater than zero? Answered by Chris Fisher. 





An equilateral triangle 
20020611 

From Sarah: Hi. My name is Sarah. I'm a secondary student taking a Math 30C course by correspondence. The question has two parts.
The first part is: Draw an equilateral triangle XYZ. Draw the altitude from X to YZ. Choose any point P inside the triangle or on the triangle. Draw perpendiculars from P to the sides of the triangle. The Second part is:
Measure the altitude h and the 3 perpendiculars s, t, and u to the nearest mm. Repeat as many time as is necessary until you can state a generalization concerning h, s, t, and u. If you could help me, it would be greatly appreciated. Answered by Penny Nom. 





Isoscles and scalene 
20010417 

From Autumn: explain where the term isoscles and scalene came from? Answered by Chris Fisher. 





Constructing an equilateral triangle 
20010414 

From Peggy: Please send directions to make an equilateral triangle in plane geometry. I want each student to draw two, cut them out, and place them together to form a Jewish Star. Answered by Penny Nom. 





Equilateral 
20010125 

From A student: I AM 9 YEARS OLD AND I HAVE HOMEWORK. I WOULD LIKE TO KNOW IF THERE IS SUCH A THING AS A EQUILATERAL SQUARE. Answered by Penny Nom. 





An equilateral triangle in a circle 
20000311 

From Michael Setlik: An equilateral triangle is drawn within a circle such that all three points of the triangle just touch the inside of the circle. Given the diameter of the cicle as six inches what is the length of the sides of the triangle? Answered by Harley Weston. 





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. 





An equilateral triangle on a square 
19990426 

From Ed: My Grade 8 class and I were discussing the solution to the following problem: What is the area of the largest equilateral triangle that can be drawn on a 5 cm square. We used 5 cm as the base of our triangle and then drew the other two legs of 5 cm each to make the equilateral triangle. We then drew an altitude from the upper vertex to the base of the triangle. Using the law of Pythagoras with side a of 2.5 and side c of 5 we calculated side b to be 4.3 cm (the altitude). Therefore the area of the triangle would be 5 x 4.3 divided by 2 or 10.75 square cm. The answer key to this resource says I am wrong. What do you think? Have we interpreted the question incorrectly? Answered by Chris Fisher and Harley Weston. 





Area of a triangle. 
19980201 

From Jodi Blucher: Is there a formula for the area of an equilateral triangle knowing the length of the sides? Answered by Chris Fisher and Harley Weston. 





Un triangle équilatéral 
20021027 

From Un eleve: Soit ABC un triangle équilatéral construit dans le sens direct. Le point D est symétrique de A par rapport à la droite (BC), et le point E est symétrique de B par rapport au point C. L'intersection des droites (AD) et (BC)est notée H. On pose AB=a.  Je dois calculer les longueurs AD et AE en fonction de a.
 Je dois montrer que le triangle ADE est équilatéral. J'arrive a prouver qu'il est isocèle en E mais j'aimerai trouver que AD=DE.
Answered by Claude Tardif. 

