How to find the area of an acute / obtuse isosceles triangle - ACT Math
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What is the area of an isosceles triangle with a vertex of 
degrees and two sides equal to 
?
What is the area of an isosceles triangle with a vertex of
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:
or 
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
Now, based on the properties of an isosceles triangle, you can draw the following as well:
Based on your standard reference
Therefore,
This means that
Now, the area of the triangle is:
Compare your answer with the correct one above
An isosceles triangle has a height of 
and a base of 
. What is its area?
An isosceles triangle has a height of
Use the formula for area of a triangle:
Use the formula for area of a triangle:
Compare your answer with the correct one above
An isosceles triangle has a base length of 
and a height that is twice its base length. What is the area of this triangle?
An isosceles triangle has a base length of
1. Find the height of the triangle:
2. Use the formula for area of a triangle:
1. Find the height of the triangle:
2. Use the formula for area of a triangle:
Compare your answer with the correct one above