courtcourt072 Posts: 3, Reputation: 1 New Member #1 Sep 22, 2007, 08:39 PM
aread of the circle inscribed a square.
Suppose you are given a square with an inscribed circle as shown below. If the area of the square is 85 m2 what is the area of the circle? (use 3.14159 as your approximation for Pi and round your answer to two decimal places)
 galactus Posts: 2,271, Reputation: 282 Ultra Member #2 Sep 23, 2007, 10:02 AM
This is very straightforward. I assume the circle is touching the sides of the square, since you didn't include "as shown below".

The sides of the square can be found by $x^{2}=A$. You are given A. Solve for x. Half that will be the radius of the circle.
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 MOWERMAN2468 Posts: 3,214, Reputation: 243 Ultra Member #3 Sep 23, 2007, 10:04 AM
 kbc89usna Posts: 1, Reputation: 1 New Member #4 Nov 11, 2010, 08:03 AM
The area of a square is the square of its sides (length of "a"). 85 = a(squared) so a = square root(85) = 9.2195. Draw a diagonal from the corners of the square to for two triangles. This diagonal will be the hypotenuse ("c") of the triangles and the diameter of the circle ("d"). Use Pythagorean Theorem a (squared) + b(squared) = c (squared) for the length of the diagonal. Since this is a square "a" and "b" in the Pythagorean Theorem are equal. 2*"a “squared = "a “squared = " squared.
2 * 9.2195(squared) = " squared.
2 * 9.2195(squared) = "(squared). C = square root (2 * 84.9991)= 13.0383. This means the diameter of the circle is 13.0383 so the radius is 13.0383/2 = 6.5192. The area of the circle is 6.5192(squared) * pi. = 6.5192(squared) * 3.14159 = 133.5164524470612

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