Answer:
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 12m
- 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 = [tex]\frac{7}{2}[/tex] 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[tex]\frac{\pi r^{2} }{2}[/tex]
Area of band= Area of big semi-circle- Area of small semi-circle
= [tex]\frac{\pi 7^{2}-\pi 3.5^{2} }{2}[/tex]
=[tex]\frac{36.75\pi}{2}[/tex]
=57.73 m²
Area of the shaded region= 2*area of rectangle+area of semi-Circular band
=[tex]2*42+57.73[/tex]
=141.73 m²
