Bunuel wrote:
In the figure above, four equal circles are drawn within a square whose perimeter is 32. What is the area of the shaded region?
A. 32 − 16π
B. 64 − 16π
C. 64 − 32π
D. 32π − 32
E. 64π − 64
Attachment:
2016-01-31_1802.png
Whenever you see a question with shaded area, try to find out the area of the participating figures
Area of the shaded region = area of the square - the area of 4 circles.
1. Area of square.
We are given that the perimeter = 32.
Since perimeter of square = 4*sides.
Therefore side = 8
Area = 8*8 = 64
2. Area of Circles:
Since the circles are all the same. we can just find the area of one and multiply it with 4
The diameter of 2 circles = side of the square.\ = 8
Therefore diameter of one circle = 8/2 = 4
Therefore radius of one circle = 4/2 = 2
Area of one circle = π*\(2^2\) = 4π
Area of 4 circles = 4*4π = 16π
Area of shaded region = area of square - area of 4 circles = 64 - 16π
Option B