Question

Determine the perimeter and area of the unshaded portion of the figure below, given

the circle diameter of 7 cm and the perimeter of the entire figure is 42 cm.
Note: the red area in the image is the same as the unshaded area in the exam
question.

Answer 1

The perimeter of the un-shaded portion is 42 cm

Explanation:

The given information are;

The diameter of the circle = 7 cm

The perimeter of the entire figure = 42 cm.

The formula for the perimeter = 2 semi circles + 2 Side lengths, l

The formula for the perimeter = 2 × π·D/2 + 2× l

42 = 2×π·7/2 + 2·l = π·7 + 2·l

2·l = 42 - π×7 = 20.009 cm

l = 20.009 cm/2 = 10.004 cm

The perimeter of the un-shaded portion,
`P_((unshaded))` = 2 side length + 2 semicircles

∴
`P_((unshaded))` = 2×l + 2 × π·D/2 = 2×l + 2×π·7/2 = 2·l + π·7 = 2×10.004 + π×7

`P_((unshaded))` = 41.999 ≈ 42 cm

Therefore, the perimeter of the un-shaded portion = 42 cm.