Question

Find the area of the unshaded part of the figure

Answer 1

Answer:

  unshaded area = 25(4 -π) in^2 ≈ 21.46 in^2

Step-by-step explanation:

Each of the shaded circles has a diameter of (20 in)/4 = 5 in, which also is the width of the enclosing rectangle. Then each circle has a radius of 2.5 in, and an area of ...

  A = πr^2 = π(2.5 in)^2 = 6.25π in^2

The four circles together have an area of ...

  4A = 4·(6.25π in^2) = 25π in^2

The area of the rectangle is the product of its length and width:

  A = LW = (20 in)(5 in) = 100 in^2

Since the circles are shaded, the unshaded area is the difference between the rectangle area and the total area of the four circles:

  unshaded area = (100 in^2) - (25π in^2) = 25(4 -π) in^2 ≈ 21.46 in^2