How to find the area of a 45/45/90 right isosceles triangle - ACT Math
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What is the area of an isosceles right triangle with a hypotenuse of 
?
What is the area of an isosceles right triangle with a hypotenuse of
Now, this is really your standard 
triangle. Since it is a right triangle, you know that you have at least one 
-degree angle. The other two angles must each be 
degrees, because the triangle is isosceles.
Based on the description of your triangle, you can draw the following figure:
This is derived from your reference triangle for the 
triangle:
For our triangle, we could call one of the legs 
. We know, then:
Thus, 
.
The area of your triangle is:
For your data, this is:
Now, this is really your standard
Based on the description of your triangle, you can draw the following figure:
This is derived from your reference triangle for the
For our triangle, we could call one of the legs
Thus,
The area of your triangle is:
For your data, this is:
Compare your answer with the correct one above
What is the area of an isosceles right triangle with a hypotenuse of 
?
What is the area of an isosceles right triangle with a hypotenuse of
Now, this is really your standard triangle. Since it is a right triangle, you know that you have at least one -degree angle. The other two angles must each be degrees because the triangle is isosceles.
Based on the description of your triangle, you can draw the following figure:
This is derived from your reference triangle for the triangle:
For our triangle, we could call one of the legs . We know, then:
Thus, 
.
The area of your triangle is:
For your data, this is:
Now, this is really your standard
Based on the description of your triangle, you can draw the following figure:
This is derived from your reference triangle for the
For our triangle, we could call one of the legs
Thus,
The area of your triangle is:
For your data, this is:
Compare your answer with the correct one above
What is the area of an isosceles right triangle with a hypotenuse of 
?
What is the area of an isosceles right triangle with a hypotenuse of
Now, this is really your standard triangle. Since it is a right triangle, you know that you have at least one -degree angle. The other two angles must each be degrees because the triangle is isosceles.
Based on the description of your triangle, you can draw the following figure:
This is derived from your reference triangle for the triangle:
For our triangle, we could call one of the legs . We know, then:
Thus, 
.
The area of your triangle is:
For your data, this is:
Now, this is really your standard
Based on the description of your triangle, you can draw the following figure:
This is derived from your reference triangle for the
For our triangle, we could call one of the legs
Thus,
The area of your triangle is:
For your data, this is:
Compare your answer with the correct one above
is a right isosceles triangle with hypotenuse 
. What is the area of 
?
Right isosceles triangles (also called "45-45-90 right triangles") are special shapes. In a plane, they are exactly half of a square, and their sides can therefore be expressed as a ratio equal to the sides of a square and the square's diagonal:
, where 
is the hypotenuse.
In this case, 
maps to 
, so to find the length of a side (so we can use the triangle area formula), just divide the hypotenuse by 
:
So, each side of the triangle is 
long. Now, just follow your formula for area of a triangle:
Thus, the triangle has an area of 
.
Right isosceles triangles (also called "45-45-90 right triangles") are special shapes. In a plane, they are exactly half of a square, and their sides can therefore be expressed as a ratio equal to the sides of a square and the square's diagonal:
In this case,
So, each side of the triangle is
Thus, the triangle has an area of
Compare your answer with the correct one above