Question

In fig. three semicircles A, B and C are drawn having diameters 14cm each and
a circle D is drawn with diameter 28cm. Find the perimeter of the shaded
region.
​

Answer 1

Given :- In fig. three semicircles A, B and C are drawn having diameters 14cm each and a circle D is drawn with diameter 28cm. Find the perimeter of the shaded region.

Solution :-

Perimeter of shaded region :-

• Perimeter of large semi - circle + Perimeter of circle D + 3(Perimeter of semi - circles A , B and C.)

given that,

• Diameter of large semi - circle = Diameter of circle A , B and C = 14 + 14 + 14 = 42 cm.
• Diameter of circle D = 28 cm.
• Diameter of circle A , B and C = 14 cm.

we know that,

• radius = (Diameter /2) .

so,

• Radius of large semi - circle = 42/2 = 21 cm.
• Radius of circle D = 28/2 = 14 cm.
• Radius of circle A , B and C = 14/2 = 7 cm.

we also know that,

• Perimeter of circle = 2 * π * radius .
• Semi - perimeter of circle = π * radius .

then,

→ Perimeter of shaded region = π * 21 + 2 * π * 14 + 3(π * 7) = 21π + 28π + 21π = 70π = 70 * (22/7) = 220 cm . (Ans.)

Hence, Perimeter of shaded region will be 220 cm.

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