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Question

In fig., 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. The area of the shaded region is _____. (Use π=3.14).


A
37.25 cm2
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B
38.25 cm2
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C
39.25 cm2
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D
40.25 cm2
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Solution

The correct option is C 39.25 cm2
Since,
ABC is an equilateral triangle.
A=B=C=60o

Area of sector, AF EA
=π360×πr2 cm2
=(60o360o×π(5)2)cm2
=256π cm2

Areas of all three sectors are equal.
Total area of shaded region =3(256π) cm2
=25×3.142
=39.25 cm2

Area of shaded region =39.25 cm2

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