maths question?

Question

go onto this site and do problem number 8
http://www.hamilton.ie/mathschallenge/Wk3.htm

Answer 1

Can I draw your attention to the competition rules:

"Competitors must solve the puzzles themselves without outside assistance. "

Go to.

Answer 2

Let the region above region I be denoted III, and let the region to the right of I be denoted IV. Let r denote the radius of the intersecting semicircles. Then 2r is the radius of the larger quarter-circle. Then the area of the quarter-circle is given by

I + II + III + IV = (1/4)π(2r)² = πr²

The area of the two semicircles is given by

(I+III) + (I+IV) = 2*(½ πr²) = πr²

Therefore

I + II + III + IV = I + III + I + IV

so

II = I

(I've used I, II, etc. to denote regions as well as their areas, but I'm sure you understand.)

Answer 3

=1
S1: the area of region I
S2:the area of region II
=>S2 =(pi*R^2)/4 - (2*pi*R^2)/8 +S1
=>S1 =S2