Question

Find the area of the shaded region given in figure

Answer 1

ABCD is a square of side 14 cm.

Join JK, KL, LM and MJ.

There are four equal semi-circles and JKLM formed a square.

∴ FH = 14 – (3 + 3) = 8 cm

So, the side of square JKLM is 4 cm and radius of semi-circle of both ends are 2 cm each.

∴ Area of square JKLM = (4)² = 16 cm²

Area of semi-circle HJM = `(π"r"^2)/2`

= `(π xx (2)^2)/2`

= 2π cm²

∴ Area of four semi-circles

= 4 × 2π

= 8π cm²

Now, area of square ABCD = (14)² cm² = 196 cm²

∴ Area of shaded region = Area of square

ABCD – [Area of four semi-circles + Area of square JKLM]

= 196 – [8π + 16]

= 196 – 16 – 8π

= (180 – 8π) cm²

Hence, the required area of the shaded region is (180 – 8π) cm².