# ACT Math : How to find the area of a 45/45/90 right isosceles triangle

## Example Questions

### Example Question #5 : Isosceles Triangles

What is the area of an isosceles right triangle with a hypotenuse of ?

Explanation:

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:

### Example Question #6 : Isosceles Triangles

What is the area of an isosceles right triangle with a hypotenuse of ?

Explanation:

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:

### Example Question #7 : Isosceles Triangles

What is the area of an isosceles right triangle with a hypotenuse of ?

Explanation:

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:

### Example Question #8 : Isosceles Triangles

is a right isosceles triangle with hypotenuse . What is the area of ?