Question

The shape shown consists of three sides of a rectangle together with a semicircle. Which of the following is

closest to the perimeter of the shape? (The dashed line is not a part of the perimeter.
(1) 56.1
(2) 44.6
(3) 38.3
(4) 32.5

Answer 1

The perimeter of the figure is 32.5 ⇒ (4)

Explanation:

Let us solve the question

From the given figure

∵ The perimeter of the figure is the sum of the 3 sides of the rectangle

and the length of the circumference of the semicircle

∴ P = W + L + W +
`(1)/(2)` C, where W is the width, L is the length, and C is the

circumference of the circle

∵ W = 3.4 and L = 10

∵ C = π d, d is the diameter of the

∵ The diameter of the circle equal to the length of the rectangle

∴ d = L = 10

∴ C = π(10) = 10π

→ Substitute the values of W, L, and C in the rule of the perimeter above

∵ P = 3.4 + 10 + 3.4 +
`(1)/(2)` (10π)

→ Use π = 3.14

∴ P = 3.4 + 10 +3.4 + 15.7

∴ P = 32.5

∴ The perimeter of the figure is 32.5