Question

Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use
in any formulas used.

An image shows a 8-inch square with a semicircle attached to each of the four sides of the square so that the square is enclosed by the semicircles. The diameter of each semicircle is the same as the length of each side of the square of 8 inches.


Perimeter
inches, Area
square inches


Perimeter
inches, Area
square inches


Perimeter
inches, Area
square inches


Perimeter
inches, Area
square inches

Answer 1

Let r = 4 in (half of the 8-in side). Semicircle arc length = πr and area = (1/2)πr^2.

Perimeter = 4 × (arc length) = 4(πr) = 4π(4) = 16π in ≈ 50.27 in.

Area = area of square + 4 × (area of one semicircle)
= 8^2 + 4[(1/2)πr^2] = 64 + 2π(16) = 64 + 32π in^2 ≈ 164.53 in^2.