SOLUTION: PLEASE HELP- Whats the area of the shaded figure? Round your answer to the nearest tenth. Can anyone show me step by step how to figure this out? 12.5cm is in the inside. 8.4 is

Algebra ->  Surface-area -> SOLUTION: PLEASE HELP- Whats the area of the shaded figure? Round your answer to the nearest tenth. Can anyone show me step by step how to figure this out? 12.5cm is in the inside. 8.4 is       Log On


   



Question 655352: PLEASE HELP-
Whats the area of the shaded figure? Round your answer to the nearest tenth.
Can anyone show me step by step how to figure this out? 12.5cm is in the inside. 8.4 is at the bottom. THANKS!
http://i46.tinypic.com/2u8koes.png < picture of the problem with multiple choice answers

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
if you look closely at shaded area, you will see that that area could be calculated as following:
you have a square inside ellipse with sides 12.5cm and 8.4cm, so its
area is:
Area_square+=12.5cm%2A8.4cm
Area_square+=105cm%5E2
than you have two half circles with same diameter of 8.4cm that you should deduct from the area of the square, and these two halves make one full circle with area C=r%5E2pi where r=8.4cm%2F2=4.2cm
so, we have
Area_circle1+=+r1%5E2pi
Area_circle1+=+%284.2cm%29%5E2%2A3.14
Area_circle1+=+55.3896%5E2cm%5E2
find their difference:
Area_square+-Area_circle1=105cm%5E2-55.3896%5E2cm%5E2
Area_square+-Area_circle1=49.6104cm%5E2
finaly, you have two half circles, one on left and one on right side of the square, that make one full circle...its diameter is 12.5cm; so, its radius is r2=6.25cm and the area will be
Area_circle2+=+r2%5E2pi
Area_circle2+=+%286.25cm%29%5E2pi
Area_circle2+=122.65625cm%5E2

now, your shaded area will be:%28Area_square+-Area_circle1%29+%2BArea_circle2
%28Area_square+-Area_circle1%29+%2BArea_circle2=49.6104cm%5E2%2B122.65625cm%5E2
%28Area_square+-Area_circle1%29+%2BArea_circle2=172.26665cm%5E2 ...round to one decimal place

%28Area_square+-Area_circle1%29+%2BArea_circle2=172.3cm%5E2

so, your answer is 172.3cm%5E2