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

## Example Questions

### Example Question #1 : Acute / Obtuse Isosceles Triangles

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

Explanation:

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

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:

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 #1 : Acute / Obtuse Isosceles Triangles

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

Explanation:

Use the formula for area of a triangle:

### Example Question #1 : Acute / Obtuse Isosceles Triangles

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