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In figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm. To intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region. [Use $π = 3.14]$

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51.75

c m 2

74.98

c m 2

39.25

c m 2

47.54

c m 2

answer is C.

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Detailed Solution

Given that the side of the equilateral triangle ABC is 10 cm.
We have to find the area of the shaded region.

The expression to find the area of a sector is

A = π r 2 θ 360 o

, where r is the radius of a circle.
Radius of the sector containing the vertices A, B and C is

102 = 5 c m

.
As the triangle ABC is equilateral,

θ = 60 o

.
Area of the sector containing vertex B,

A 1

is,

A 1 = π r 2 θ 360 o ⇒ A 1 = 22 × 5 × 5 × 60 o 7 × 360 o ⇒ A 1 = 13.09524

Thus, the area of the shaded region, A is,

A = 3 × A 1 ⇒ A = 3 × 13.09524 ∴ A = 39.25 c m 2

The area of the shaded region is 39.25

c m 2

.
Therefore, the correct option is 3.

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