Question

Find the area of the shaded region.


PLEASE HELP

Answer 1

Area of the shaded region = 141.73 m²

Explanation:

Let the figure be divided into three 2D parts.

They are:

1. 2 rectangles of dimensions: 3.5m x 12m
2. semi-circular band

let us find the area of these parts separately

Rectangular portion:

Length= 12 m

Breadth= 3.5 m

We know that area of rectangle is equal to length x breadth

⇒area = 12 x 3.5

= 42 m²

Semi-Circular band:

Width of the band =3.5 m

Radius of inner side =
`(7)/(2)` m= 3.5 m

Radius of outer side = 3.5 + width= 3.5+3.5

=7 m

We know that area of semi-circle is
`(\pi r^(2) )/(2)`

Area of band= Area of big semi-circle- Area of small semi-circle

=
`(\pi 7^(2)-\pi 3.5^(2) )/(2)`

=
`(36.75\pi)/(2)`

=57.73 m²

Area of the shaded region= 2*area of rectangle+area of semi-Circular band

=
`2*42+57.73`

=141.73 m²