All ACT Math Resources
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 ?
Based on the description of your triangle, you can draw the following figure:
You can do this because you know:
- The two equivalent sides are given.
- 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:
Example Question #2 : Acute / Obtuse Isosceles Triangles
An isosceles triangle has a height of and a base of . What is its area?
Use the formula for area of a triangle:
Example Question #3 : 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?
1. Find the height of the triangle:
2. Use the formula for area of a triangle: