Geometry- Areas of circles, Square, Rect, Arc Lengths, Probability, Etc.?

Question

Look at the following pictures:
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part1mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part6mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part5mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part4mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part3mathtest.jpg

In order to see the pictures, In the left corner of the page there is a tab that says FULL SIZE click this and you can actually see the picture. I really don't get this stuff.
I know the equations and everything but still need help. If you could just tell me step by step how you would get the answer that would be so helpful. I want to understand this but just need some help. Thanks

http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part3mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part1mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part4mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part5mathtest.jpg
http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part6mathtest.jpg

Answer 1

Find the shaded area of the four congruent circles and the overlapping square.

Let
s = side of square
r = radius circle
A = area of all four circles

Given
s = 8

We have:

r = s/2 = 4

A = 4πr² = 4π(4²) = 4π(16) = 64π

The square fills in some area not covered by the circles. Each quarter of the square contains a quarter of a circle so the whole square contains the equivalent of one circle. The additional area needs to be added to A above.

Area square = s² = 8² = 64

Additional area = 64 - A/4 = 64 - 16π

Total shaded area = 64π + (64 - 16π) = 48π + 64

Answer 2

Lets just take the first one.

The square is 8x8. That's 64 square units.

Each circle has a radius of 4 units. The area of one whole circle is then: area = pi R^2. But, 1/4 of each circle is covered by the square, so you have only (3/4) pi R^2. Times 4, because there are 4 circles.

Total area is 64 + (3/4) (pi R^2) (4)

The other problems can be solved piece by piece, using logic just like for the first problem.

Answer 3

element of sq. is one hundred forty four. sq. root of one hundred forty four is 12 so sq. has sides 12 cm. 4 x 12 = 40 8 so perimeter is 40 8 cm. Rectangle has same perimeter, hence length is two times width so 2x + x + 2x + x = 48cm. Re-manage to 6x = 40 8. Divide 40 8 by technique of 6 to get x = 8cm. So element of rectangle is two(8) x 8 = 16 x 8 = 128 cmsq. 2 squares next to at least one yet another, aspect length 8cm, section 64cmsq so element of rectangle is 128cmsq.