How to find the area of an acute / obtuse isosceles triangle - ACT Math
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An isosceles triangle has a height of
and a base of
. What is its area?
An isosceles triangle has a height of and a base of
. What is its area?
Use the formula for area of a triangle:


Use the formula for area of a triangle:
Compare your answer with the correct one above
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 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:
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
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
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 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:


1. Find the height of the triangle:
2. Use the formula for area of a triangle:
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 and a base of
. What is its area?
Use the formula for area of a triangle:


Use the formula for area of a triangle:
Compare your answer with the correct one above
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 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:
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
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
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 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:


1. Find the height of the triangle:
2. Use the formula for area of a triangle:
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 and a base of
. What is its area?
Use the formula for area of a triangle:


Use the formula for area of a triangle:
Compare your answer with the correct one above
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 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:
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
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
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 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:


1. Find the height of the triangle:
2. Use the formula for area of a triangle:
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 and a base of
. What is its area?
Use the formula for area of a triangle:


Use the formula for area of a triangle:
Compare your answer with the correct one above
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 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:
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
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
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 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:


1. Find the height of the triangle:
2. Use the formula for area of a triangle:
Compare your answer with the correct one above
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 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:
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
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
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 and a base of
. What is its area?
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 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:


1. Find the height of the triangle:
2. Use the formula for area of a triangle:
Compare your answer with the correct one above
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 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:
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
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
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 and a base of
. What is its area?
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 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:


1. Find the height of the triangle:
2. Use the formula for area of a triangle:
Compare your answer with the correct one above
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 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:
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
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
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 and a base of
. What is its area?
Use the formula for area of a triangle:


Use the formula for area of a triangle:
Compare your answer with the correct one above