Find the area of the shaded region given in fig.

Answer:

Given parameters

Side of the square ABCD = 14 cm

Area of the square ABCD = (side)2

Area of the square ABCD = (14)2

Area of the square ABCD = 196 cm2

There are four semi-circles which mean there are two complete circles.

The radius of the semi-circles formed (r) = 2 cm

Area of the semi-circles = 4 × 1/2 (πr2)

π = 3.14

Area of the semi-circles = 4 × 1/2 (3.14 × 22)

Area of the semi-circles = 4 × 12.56/2

Area of the semi-circles = 25.12 cm2

Inside the semi – circles length of the side of square formed = 4 cm

Area of the square = 42

Area of the square = 16 cm2

Area of the shaded region = Area of the square ABCD – (Area of 4 semi-circles + Area of square)

Area of the shaded region = 196 – (25.12 + 16)

Area of the shaded region = 154.88 cm2

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