Question

Area addition and subtraction

Answer 1

3.8
`in^(2)`

Explanation:

We are given a square of size 6x6 in. So, area of this square is equal to 6 x 6 = 36
`in^(2)`. Now, the shaded region is
`(1)/(2)` x (Area of square - area of semicircles)

The diameter of both semicircles = side of the square = 6in

So, radius (r) =
`(1)/(2)` x diameter =
`(1)/(2)` x 6 = 3in

And hence, area of semicircle is =
`(1)/(2)` x π
`r^(2)`

=
`(1)/(2)` x π
`3^(2)`

Since, there are two semicircles we multiply above by 2, so area of both semicircles = 2 x
`(1)/(2)` π
`3^(2)` = 9π

Area of shaded region =
`(1)/(2)` (36 - 9π) = 3.8628 = 3.8
`in^(2)` to the nearest tenth.