ACT Math : How to find the area of an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Area Of An Acute / Obtuse Isosceles Triangle

What is the area of an isosceles triangle with a vertex of  degrees and two sides equal to ?

Possible Answers:

Correct answer:

Explanation:

Based on the description of your triangle, you can draw the following figure:

_tri71

You can do this because you know:

  1. The two equivalent sides are given.
  2. Since a triangle is  degrees, you have only  or  degrees left for the two angles of equal size. Therefore, those two angles must be  degrees and  degrees.

Now, based on the properties of an isosceles triangle, you can draw the following as well:

_tri72

Based on your standard reference  triangle, you know:

Therefore,  is .

This means that  is  and the total base of the triangle is .

Now, the area of the triangle is:

 or 

Example Question #2 : How To Find The Area Of An Acute / Obtuse Isosceles Triangle

An isosceles triangle has a height of  and a base of . What is its area?

Possible Answers:

Correct answer:

Explanation:

Use the formula for area of a triangle:

Example Question #3 : How To Find The Area Of An Acute / Obtuse Isosceles Triangle

An isosceles triangle has a base length of  and a height that is twice its base length. What is the area of this triangle?

Possible Answers:

Correct answer:

Explanation:

1. Find the height of the triangle:

2. Use the formula for area of a triangle:

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