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swat32
3 years ago
8

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

Mathematics
1 answer:
Tresset [83]3 years ago
5 0

Answer:

The perimeter of the un-shaded portion is 42 cm

Step-by-step 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.

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