SOLUTION: Square A is circumscribed about a circle by 100%. By how much is the area increased? b)A semi circle sits on top of a square. The perimeter of the figure is 36cm. Find the area

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Square A is circumscribed about a circle by 100%. By how much is the area increased? b)A semi circle sits on top of a square. The perimeter of the figure is 36cm. Find the area      Log On


   

Question 140042: Square A is circumscribed about a circle by 100%. By how much is the area increased?
b)A semi circle sits on top of a square. The perimeter of the figure is 36cm. Find the area of the figure.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Square A is circumscribed about a circle by 100%. By how much is the area increased?
:
Choose a value for r and find the percentage increase in area:
:
r = 5, then one side of the square = 10
%28pi%2A5%5E2%29%2F10%5E2 = .78 = 78% increase in area
:
:
b)A semi circle sits on top of a square. The perimeter of the figure is 36cm. Find the area of the figure.
:
Let r = radius of the half circle
Then
2r = side of the square:
:
Find r using the Perimeter:
3(2r) + .5(2*pi*r) = 36
6r + (pi*r) = 36
r(6+pi) = 36
r = 36%2F%28%286%2Bpi%29%29
r = 3.938
:
Side = 2(3.938) = 7.876
:
Area = 7.376^2 + .5*pi*3.936^2
Area = 62.03 + 24.335
Area = 86.365 sq mm