# Math Help - Is there enough info to do this problem?

1. ## Is there enough info to do this problem?

Given a figure of a square with a circle inscribed in it. If the area of the shaded region (the region outside of the inscribed circle) is 1, then find the area of the circle?

A. pi/4
B. pi
C. pi/(pi-4)
D.1/2(pi-4)
E. pi/(pi-4)^2

This is a gre quant Q

2. Let's say the side of the square is x. Then, the shaded area is given by:

$x^2 - \pi (\frac{x}{2})^2 = 1$

Solve for x. Then find the area of the square

3. I'm trying to use (2r)^2 as the area of my square but the answer won't come out that way. Why is this?

4. Oops, typo from my part. You need to find the area of the circle... not the square. Sorry

Ok, $x^2 - \pi (\frac{x}{2})^2 = 1$

So,

$x^2(1-\frac{\pi}{4}) = 1$

For ease, I'll multiply by pi and 1/4.

$\frac{x^2\pi}{4}(1-\frac{\pi}{4}) = \frac{\pi}{4}$

$\frac{x^2\pi}{4} = \frac{\pi}{4(1-\frac{\pi}{4})}$

But x^2/4 * pi is the area of the circle... so;

$Area = \frac{\pi}{4-\pi}$

Simplify if need be.

5. Originally Posted by sfspitfire23
I'm trying to use (2r)^2 as the area of my square but the answer won't come out that way. Why is this?
Should come out ok:
4r^2 - pi r^2 = 1
r^2(4 - pi) = 1
Hokay?