Mathematics: Find the area of the shaded region.

Step-by-step explanation:good answer numbers...

Find the area of the shaded region. - id4535982, nerual0503

lisapcarroll

15.01.2022

Area of the shaded region = 141.73 m²

Step-by-step explanation:

Let the figure be divided into three 2D parts.

They are:

2 rectangles of dimensions: 3.5m x 12msemi-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 = $\frac{7}{2}$ 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 $\frac{\pi r^{2} }{2}$

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

= $\frac{\pi 7^{2}-\pi 3.5^{2} }{2}$

= $\frac{36.75\pi}{2}$

=57.73 m²

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

= 2*42+57.73

=141.73 m²

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