Question

In the given figure, ABCD is a square of side `14cm`.Semicircles are drawn with each side of square as diameter. Find the area of the shaded region.

Answer 1

Let `A_1` and `A_2` are area of the shaded and unshaded regions respectively.
Let side of the square is `a` cm.
Then,
`A_1+A_2 = a^2->(1)`...[Area of square `= a^2` ]
`Also, A_1/4+A_2/2 = pi/2(a/2)^2 = (pia^2)/8`
`=>A_1+2A_2 = (pia^2)/2->(2)`
From (1),
`=>A_1+2(a^2-A_1) = (pia^2)/2`
`=>A_1 = 2a^2-(pia^2)/2`
`=>A_1 = a^2(2-pi/2)`
`=>A_1 = (14)^2(2-22/(2*7))` ... [As `a = 14`]
`A_1 = 196(3/7) = 84cm^2`
So, required area is `84 cm^2`.