# Finding the area of the shaded figure

• May 19th 2008, 08:54 PM
scorpio
Finding the area of the shaded figure
Could anyone tell me how to do these two?

http://i212.photobucket.com/albums/c...4/mathhelp.jpg<--- the side numbers are all 5's
• May 19th 2008, 09:53 PM
Behind the eight ball.
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.
• May 19th 2008, 11:57 PM
earboth
Quote:

Originally Posted by scorpio
Could anyone tell me how to do these two?

http://i212.photobucket.com/albums/c...4/mathhelp.jpg<--- 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

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

Then the shaded area is calculated by:

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

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

$\displaystyle A=A_{circle}-A_{square}=\pi \cdot (5)^2 - 4 \cdot \frac12 \cdot 5^2 = 25(\pi-2)$
• May 20th 2008, 12:43 AM