Finding the area of the shaded figure

**scorpio** · May 19th 2008, 08:54 PM

Could anyone tell me how to do these two?

<--- the side numbers are all 5's

**Bradley** · May 19th 2008, 09:53 PM

If your drawing is accurate, no.
On the other hand,
if the first is a circle inside an 8x8 square, yes.
That's 64 - area of circle with radius 4 (area = pi(r^2)).
or 64-(16)pi.

The next figure, see reply from earboth before I lead you astray.

Bye.

**earboth** · May 19th 2008, 11:57 PM

Originally Posted by scorpio

Could anyone tell me how to do these two?

<--- the side numbers are all 5's

to #2:

Unfortunately it isn't clear to me which distance is labeled 5:

1. The side of a square has the length 5. Then the diameter of the circle is

$d^2=5^2+5^2~\implies~\boxed{d=5\sqrt{2}}$

Then the shaded area is calculated by:

$A=A_{circle}-A_{square}=\pi \cdot \left(\frac{5\sqrt{2}}{2}\right)^2 - 5^2 = 25\left(\frac12\pi-1\right)$

2. The length of the radius is 5. Then the inscribed square consists of 4 isosceles right triangles. The shaded area is calculated by:

$A=A_{circle}-A_{square}=\pi \cdot (5)^2 - 4 \cdot \frac12 \cdot 5^2 = 25(\pi-2)$

**Bradley** · May 20th 2008, 12:43 AM

Thanks for pointing my mind back to the figure.

I will be using this to remind me next time I do geometry lessons with my daughter.

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Finding the area of the shaded figure

Behind the eight ball.

Diagonal across a square, diameter of circle.

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