







The height of a isosceles trapezoid 
20170403 

From Riham: Hi
How can I find the height in an isosceles trapezoid if I have the measurements of all of its sides ?
Thank u in advance. Answered by Penny Nom. 





A circle inscribed in an isosceles triangle 
20170114 

From Sal: There is a right isosceles triangle. Inscribed inside of it, is the largest possible circle.
Ho do you find the value of the radius?
I want to find out a way of only using the rules/laws of geometry, or is that not possible. Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20160325 

From NIHAL: A isosceles triangle is inscribed in a circle having sides 20cm,20cm,30cm. find the radius of circle Answered by Penny Nom. 





The angle at the vertex of an isosceles triangle 
20151125 

From Karan: I have been given an isosceles triangle. the Top angle is what i have to find out and the two sides adjacent to it are both 4.9 cm. i have been told that the area of the triangle is 4 cm^2. i have no idea how to work this out, any ideas? Answered by Penny Nom. 





The area of an isosceles triangle 
20150611 

From Pradipta: Find the area of an isosceles triangle having two equal sides of 20 cm each and angle between them 45 degree ? ( solve without trigonometric function). Answered by Chris Fisher. 





An isosceles right triangle 
20150517 

From Ari: In a 454590 triangle find the ratio of a leg to the hypotenuse Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20150323 

From Rachel: Triangle ABC is an isosceles triangle inscribed in circle O. If each leg of the triangle is 13cm and the altitude to the base of triangle ABC is 5cm, find the radius of the circle. Answered by Penny Nom. 





An isosceles triangle and an arc 
20150218 

From Sreeharsha: The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4] Answered by Penny Nom. 





An isosceles triangle 
20141231 

From ahmadmahmoud: an isoseles triangle is such that each of the base angles is twice the vertical angle.Find the angles of the triangle Answered by Penny Nom. 





A circle insubscribed in an isosceles trapezoid 
20131208 

From Bob: A circle is insubscribed in an isosceles trapezoid, with
parallel lengths of 8cm and 18cm.
What is the lengths of sloping edges and why? Answered by Robert Dawson. 





An isosceles tiangle 
20130616 

From Izzy: what's the height of an isosceles triangle which has a base of 50 m, and both of the other sides are 25 m? Answered by Penny Nom. 





The height of an isosceles triangle 
20120710 

From ken: I am trying to determine the various heights of an isosceles triangle, if each has the same base dimension and varies in the degree of the base (equal) angles. What is the method to do this?
As an example, of the base is 10, and the two equal angles are each 45 degrees, what is the height? With the same base (10), but with the two equal angles at 60 degrees, what is the height? And with the same base (10) and the two equal angles at 75 degrees, what would be the height?
I know how to calculate the degrees of the third angle (add the degrees of the known angles, and subtract from 180); but am unsure if that is needed for figuring the overall height.
And to be clear; I am not looking for the length of the sides of the triangle, but the height from the base to the top point.
Thank you! Answered by Chris Fisher. 





Drawing an isosceles triangle 
20120510 

From Nazrul: How can I draw an isosceles triangle whose each angle adjacent to the base is twice the vertex angle? Answered by Chris Fisher. 





How to find the base length of a isosceles triangle if only the sides are given? 
20120425 

From aqilah: how to find the base length of a isosceles triangle if only the sides are given? Answered by Chris Fisher. 





A circle is inscribed inside an isosceles trapezoid 
20110225 

From priyam: a circle is inscribed inside an isosceles trapezoid (with parallel sides
of length 18 cm and 32 cm) touching all its four sides.
find the diameter of the circle.
thanks for help!! Answered by Penny Nom. 





The area of isosceles triangle 
20110124 

From imraan: how to find the area of isosceles triangle by knowing only its sides 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 base of an isosceles triangle 
20101024 

From Brian: how can I find the base of an isosceles triangle from the height and the perimeter? Answered by Penny Nom. 





A water trough 
20101022 

From Jasmine: A water trough is 8 m long and its crosssection is an isosceles
trapezoid which is 90 cm wide at the bottom and 120 cm wide
at the top, and the height is 30 cm. The trough is not full.
Give an expression for V , the volume of water in the trough in cm^3,
when the depth of the water is d cm. Answered by Stephen La Rocque. 





The altitude of a triangle 
20100508 

From kylie: the vertex angle of an isosceles triangle is 57 degrees 24 minutes and each of its equal sides is 375.5 feet long. find the altitude of the triangle Answered by Penny Nom. 





An isosceles trapezoid is inscribed in a circle 
20100406 

From Abby: An isosceles trapezoid whose bases have lengths 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid Answered by Penny Nom. 





An isosceles triangle 
20100211 

From Kim: I am given the length of the two legs of an isosceles triangle (8), and the base angles are 30 degrees...I am asked to find the area of the triangle with only this information Answered by Tyler Wood. 





An impossible isosceles triangle 
20100131 

From Hailey: An isosceles triangle has one angle that measures 50 degrees and another that measures 70 degrees. Why can't this triangle be drawn? Answered by Penny Nom. 





An isosceles triangle 
20100128 

From Jazzy: An isosceles triangle is a 2 congruent (equal) sides. Of the third side is three times the length of the congruent side(s), and the perimeter is 75 cm, find the length of all three sides of the triangle Answered by Penny Nom. 





A triangle with two equal medians 
20091219 

From Nazrul: If two medians of a triangle are equal , how can I prove that the triangle is isosceles. Answered by Chris Fisher. 





The height of an isosceles triangle 
20091206 

From Carl: What is the height of an isosceles triangle if its base is 12cm, and its base angle is 72degrees? Answered by Penny Nom. 





An isosceles trapezoid 
20091112 

From lyjah: what is parallel sides of an isosceles trapezoid measure 5cm and 11cm long.and
oneof the other sides also measures s5cn long what of the isosceles trapeziod Answered by Penny Nom. 





An isosceles triangle 
20090809 

From Megan: Find the perimeter of an isosceles triangle with a verticle angle of 100 degrees and a base of 25 cm.
I think I could answer this if I knew what a verticle angle was.
Thanks Answered by Stephen La Rocque. 





Constructing an isosceles triangle 
20090727 

From Sanjay: How to construct an isosceles triangle ABC with a base BC = 5.4 centimetre and altitude AD = 4.7 centimetre? Please help. Answered by Janice Cotcher. 





Two questions from math class 
20090618 

From Con: Hello,
My name is Con and my son is required to answer the following questions for his maths class.
He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct?
He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution?
Q1.
Digits 2, 3, 4, 5 and 7 are each used once to compose a 5digit number abcde such that 4 divides a 3digit number abc, 5 divides a 3digit number bcd and 3 divides a 3digit number cde. Find the 5digit number abcde.
Q2.
Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD.
Con Answered by Chris Fisher. 





The central angle of a chord 
20090406 

From Dale: How do I find the central angle if I only have the cord length and radius. Answered by Harley Weston. 





An isosceles triangle 
20090326 

From sela: An isosceles triangle has two equal sides of length 10 cm. Theta is the
angle between two equal sides.
a) Express area of a triangle as a function of theta
b) If theta is increasing at a rate of 10 degrees/minute, how fast is area
changing at the instant theta=pi/3?
c) at what value of theta will the triangle have the maximum area?
Answered by Penny Nom. 





The base and height of an isosceles triangle 
20090323 

From Chris: How do you find the base and height of an isosceles triangle that has 2cm legs? Answered by Harley Weston. 





The height of an isosceles triangle 
20090129 

From Mariah: An isosceles triangle has sides 10cm, 10 cm and the base 4cm.
How do you find out the height of the triangle? Answered by Penny Nom. 





The area of an isosceles triangle 
20090119 

From faris: how to calculate area of isosceles triangle with two angles of 45 degree and base of 6 Answered by Penny Nom. 





The area of an isosceles triangle 
20081202 

From prateet: the area of an isosceles triangle is 60 sq cm and one of its equal sides is 13 cm. Find the base of the triangle. Answered by Penny. 





The diagonals of an isosceles trapezoid 
20081114 

From hazel: how to solve the diagonals of an isosceles trapezoid? what is the formula? Answered by Harley Weston. 





A garden in the shape of an isosceles triangle 
20080912 

From Rita: Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his garden will be 55 square yards, find, to the nearest tenth of a degree, the three angles of the triangle. Answered by Penny Nom. 





The length of an arc 
20080904 

From Angie: Segment PR is a diameter of circle S. If angle P =3D 25, find minor
arc QR.
This circle has an isosceles triangle in it, it is connected to the
diameter, Answered by Harley Weston. 





An isosceles triangle inscribed in a circle 
20080715 

From Anne: Here is the math problem quoted from book:
"An isosceles triangle is inscribed in a circle of radius R,
where R is a constant. Express the area within the circle but outside
the triangle as a function of h, where h denotes the height of the triangle." Answered by Penny Nom. 





The height of an isosceles triangle 
20080622 

From Evelyn: Hi! I am facing problem finding the height of the isosceles triangle. Answered by Penny Nom. 





An isosceles triangle 
20080507 

From Jay: Given: An Isosceles Triangle with the area=16m squared. What would be the length of each leg. Answered by Stephen La Rocque. 





An isosceles right triangl 
20080409 

From Stephanie: An isosceles right triangle has an area of 35 sq cm. What are the lengths of the sides? Answered by Walter Whiteley. 





The base of an isosceles triangle 
20080224 

From tahrima: find the base of an isosceles triangle whose area is 12sq.cm and the length of 1 of the equal sides is 5 cm. Answered by Stephen La Rocque. 





Finding the area of an isosceles triangle given one angle and the inradius 
20080124 

From Saurabh: Given an isosceles Triangle, whose one angle is 120 and inradius is √3. So area of triangle is? Answered by Stephen La Rocque. 





Calculate the two possible lengths of the third side. 
20071228 

From Lisa: An isosceles triangle has an area of 25.6 sq cm.
The two equal sides are 8.4 cm long.
Calculate the two possible lengths of the third side. Answered by Penny Nom. 





An isosceles triangle 
20071126 

From Nancy: I needed to help my 9th grade daughter regarding a geometry problem. After a while I realized I am not getting anywhere. I saw that in 2005 someone asked the same question and you gave them a hint. Unfortunately it still did not help. Because I had figured that much!Can you kindly help me proof this problem?
PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles?
I am sure it is something simple I am missing, but I just can not seem to be able to see it. Thank you much. Answered by Harley Weston. 





The height of an isoceles triangle 
20071029 

From Maura: I am trying to calculate the height of an isoceles triangle but in this case AB is not equal to AC.
How do I calculate this?
Thank you,
Maura age 13 Answered by Stephen La Rocque. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





Area of a star in a regular pentagon with side length 10cm 
20070724 

From Chetna: A regular pentagon with side 10 cm has a star drawn within (the vertices match).
What is the area of the star? Answered by Stephen La Rocque. 





The isosceles triangle of largest area with perimeter 12cm 
20070716 

From sharul: find the dimension of isosceles triangle of largest area with perimeter 12cm Answered by Harley Weston. 





A regular octagon is made up of 8 identical isosceles triangles 
20070604 

From Alex: A regular octagon is made up of 8 identical isosceles triangles. If the perimeterof each isosceles triangle and the hexagon are 58 cm and 168 com respectively, find the length of the identical sides of the triangle. Answered by Stephen La Rocque. 





Area of an isosceles triangle 
20070601 

From Josh: In a previous question answered by Sue regarding the area of a regular polygon you gave a formula for the area of an isosceles. My question is how did you get this formula? Can you please explain to mean the process that you used to get that formula?
Thanks Answered by Stephen La Rocque. 





Finding the area of a regular polygon 
20070504 

From Dana: We are trying to figure the square footage of a tetradecagon....sort of a round house with 14 sides that are 8 ft' in length. It has a height of 9 ft. How do we figure the square footage of this? Answered by Stephen La Rocque. 





I have an isosceles triangle. 
20070410 

From Stephanie: I have an isosceles triangle. The two equal sides are given to me, but not the
base. The equal sides are 12. I have to find the base of the triangle. Help!! Answered by Stephen La Rocque. 





An isosceles Triangle 
20070315 

From Devon: The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs. Answered by Stephen La Rocque. 





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. 





The height of an isosceles triangle 
20070127 

From Brendan: I need to find the height of an isosceles triangle whose angles are 52, 52 and 76 degrees. The base is 100, and the two equal sides are unknown. How would I go about this? Answered by Stephen La Rocque. 





An isosceles triangle 
20061229 

From Katrina: Is there any way to calculate the height or the length of the equal sides of an isosceles triangle given only the base length and the angles? Answered by Penny Nom. 





The length of the third side of a 45 degree Isosceles triangle 
20060920 

From Rusty: what is the formula to determine the length of the third side of a 45 degree Isosceles triangle? 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 do i get the height of an isosceles triangle? 
20060829 

From Luis: How do i get the height of an isosceles triangle? Answered by Penny Nom. 





Isoperimetric quotients 
20060707 

From Jessica: How do you work out an algebraic equation for the IQ of an isosceles triangle. Answered by Penny Nom. 





The height of an isosceles triangle 
20060401 

From Chris: how do you work out the height of an isosceles triangle if i know the length of the base but i don't know any angles or the lengths of the sides? Answered by Penny Nom. 





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. 





An isosceles triangle 
20051114 

From Chris: PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles? Answered by Chri Fisher. 





An isosceles triangle...with 
20050423 

From Shannon: If given an isosceles triangle...with
Is there any possible way to do this, without knowing a side, if so, please
explain in detail. Answered by Chris Fisher. 





The diaonals of an isosceles trapezoid are congruent 
20050202 

From Daniel: I am currently unable to find a proof that the diaonals of an isosceles trapezoid are congruent. Might you happen to have one? Answered by Walter Whiteley. 





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





An isosceles trapezoid 
20040831 

From Bruce: An isosceles trapezoid with bases of lengths 12 and 16 is inscribed in a circle with a radius of 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid. 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. 





An isosceles triangle 
20021030 

From Stan: What two different base lengths can an isosceles triangle have with sides on both remaining at 13 inches? How do I show this? Answered by Paul Betts and Peny Nom. 





The isosceles triangle of smallest area 
20020308 

From Lettie: can you find the isosceles triangle of smallest area that circumscribes a circle of radius of one? 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. 





Isosceles trapezoid formula 
19980512 

From Donna McMullin: The teacher of Gifted and Talented Math has been trying to locate the formula for anisosceles trapezoid and we can't find it anywhere. Could it be the same formula for that of a parallelogram ? Please advise. Answered by Walter Whiteley. 

