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Question
Find the perimeter and area of the shaded portion of the following diagram; give your answer correct to 3 significant figures. (Take π = 22/7).
Solution
Area of rectangle = 28 m x 26 m = 728 m2
(i) Perimeter of the shaded position
= 2 x 28 + 2 x 26 - 4 x 20 + 2 x `22/7` x 10
= 56 + 52 - 80 + `440/7`
= 108 - 80 + 62.85
= 170.85 - 80
= 90.85 m.
(ii) Area of one corner (unshaded) = `1/4` π x (10)2
= `1/4` x (3.14)(100 m2)
= `314/4`
= 78.5 m2
∴ Area of 4 corners (unshaded) = 78.5 x 4 = 314 m2
∴ Area of the shaded portion = [728 - 314] m2 = 414 m2.
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