A semicircle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangle measures 4 centimeters. The area of the figure is 41.4 square centimeters.

Question

What is the length of the longer side of the rectangle?

Use 3.14 for π.

Enter your answer as decimal in the box.

Answer 1

The area of the rectangle can be calculated by adding the area of the rectangle and the area of the semicircle.

Area of rectangle = length x width
Area of rectangle = x x 4

Area of semicircle = 1/2 x π x r^2
Area of semicircle = 1/2 x 3.14 x (4/2)^2

Total area = 41.4 cm^2
41.4 = x(4) + 1/2(3.14)(2^2)
41.4 = 4x + 6.28
4x = 35.12
x = 8.78

Therefore, the longer side of the rectangle is 8.78 centimeters.