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Mathematics

If the area of the semi-circular region is 77 cm2, find its perimeter.

Mensuration

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Answer

Let radius = r cm.

Given,

Area of semi-circular region = 77 cm2

∴πr22=77⇒πr2=154⇒227×r2=154⇒r2=154×722⇒r2=49⇒r=49=7 cm.\therefore \dfrac{πr^2}{2} = 77 \\[1em] \Rightarrow πr^2 = 154 \\[1em] \Rightarrow \dfrac{22}{7} \times r^2 = 154 \\[1em] \Rightarrow r^2 = \dfrac{154 \times 7}{22} \\[1em] \Rightarrow r^2 = 49 \\[1em] \Rightarrow r = \sqrt{49} = 7 \text{ cm}.

Perimeter of semi-circle = (π + 2) = πr + 2r

= 227×7+2×7\dfrac{22}{7} \times 7 + 2 \times 7

= 22 + 14

= 36 cm.

Hence, perimeter of circle = 36 cm.

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