SOLUTION: what is the area of an inscribed square whose radius is 8 inches?

Question 203382: what is the area of an inscribed square whose radius is 8 inches?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Better wording would be: What is the area of a square inscribed in a circle whose radius is 8 inches? If this is your problem then , the picture looks like:

Since the area of a square is the square (hence the term) of the side, we need to find the side of the square. As I hope you can see, finding the leg of the right triangle will help us find the side of the square.

In all 45-45-90 triangles the ratio of the hypotenuse to a leg is . In the 45-45-90 right triangle shown, the hypotenuse is 8. Substituting this into the ratio we can find the leg (using x for leg because "l" can be confused with "1"):
Multiplying both sides by x

Divide both sides by sqrt(2):

Now the leg, x, is 1/2 of the side of the square, s. So the side of the square is twice as much:

square inches.
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