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 

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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.

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Explanation:

*

*

*

*

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

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Simplify.

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

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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 

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

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Possible Answers:
Correct answer:

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Explanation:

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

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,

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, and

*

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In this equation,

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 is the length of the triangle”s base,

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 is equal to its height, and

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 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 

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, and you can rewrite the Pythagorean theorem like this:

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Rearrange the equation so that

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

*

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Next, take the square root of both sides.

*

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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:

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

*

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Solve.

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