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Q.

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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a

39.25 c m^{2}

b

11 c m^{2}

c

12 c m^{2}

d

30 c m^{2}

answer is A.

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Detailed Solution

Given that, the arcs 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.
We know that, the area of sector is

θ 360 × π r 2

.
It is given that it is equilateral triangle so the angle will be 60° of all 3 sides.
And lets divide the triangle into 3 sectors AFE, BFD and CDE.
Calculating the area sector 1.

Area sector 1 = θ 360 ° π r 2

⇒ π × 25 6

⇒ 3.14 × 25 6

Angle and radius is same so, the area of all three sectors will be same.
Calculating the area of all 3 sectors,

3 × A r Sector 1 = 3 × 3.14 × 25 6

\Rightarrow

157 × 25

\Rightarrow

39.25 c m 2

Therefore, area of the shaded region is

39.25 c m 2 .

Hence the correct option is 1.

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