Mathematics
In the figure (ii) given below, ABC is an equilateral triangle of side 8 cm. A, B and C are the centers of circular arcs of equal radius. Find the area of the shaded region correct upto 2 decimal places.
Mensuration
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Answer
We know that
△ABC is an equilateral triangle of side 8 cm
A, B, C are the centres of three circular arcs of equal radius
Radius = = 4 cm
By formula,
Area of △ABC =
= × 8 × 8
=
=
= 16 × 1.732
= 27.712 cm2.
So, the area of 3 equal sectors of 60° whose radius is 4 cm = 3 × πr2 ×
= 3 × 3.142 × 4 × 4 ×
= 3.142 × 8
= 25.136 cm2.
Area of shaded region = Area of equilateral triangle - Area of 3 sectors
= 27.712 – 25.136
= 2.576 ≈ 2.58 cm2.
Hence, area of shaded region = 2.58 cm2.
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