# Geometry 45-45-90 Triangles, How To Use The Special Right Triangle 45

Find the area of the triangle if the radius of the circle is

Substitute in the value of the radius to find the length of the diameter.

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Explanation:

Substitute in the value of the radius to find the length of the diameter.

Explanation:

Substitute in the value of the radius to find the length of the diameter.

Explanation:

Substitute in the value of the radius to find the length of the diameter.

Explanation:

Substitute in the value of the radius to find the length of the diameter.

Explanation:

Substitute in the given hypotenuse to find the length of the leg of a triangle.

Simplify.

Now, recall how to find the area of a triangle.

Since we have a right isosceles triangle, the base and the height are the same length.

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Solve.

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If the hypotenuse of an isosceles right triangle is

cm, what is the area of the triangle in square centimeters?

Explanation:

Isosceles right triangles are special triangles because they possess angles of the following measures:

,

, and

In this equation,

is the length of the triangle”s base,

is equal to its height, and

is equal to the length of its hypotenuse. In an isosceles right triangle, the base and the height have the same length; therefore,

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is equal to

, and you can rewrite the Pythagorean theorem like this:

Rearrange the equation so that

is isolated on one side of the equals sign. First, simplify by dividing both sides of the equation by 2.

Next, take the square root of both sides.

Now, plug in the value of the hypotenuse to find the height/base of the given triangle.

Now, recall how to find the area of a triangle:

Since the base and the height are the same length, we can find the area of the given triangle.

Solve.

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