## Example Questions

### Example Question #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle

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 #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle

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 #141 : 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 #4 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle is a right isosceles triangle with hypotenuse . What is the area of ?      Explanation:

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 .

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