Question

Find area of the shaded portion of the figure ​

Answer 1

`\sf C) \quad 57 \frac34 \:cm^2`

Explanation:

To find the shaded area, subtract the area of the semicircle from the area of the rectangle.

Formulae

`\textsf{Area of a rectangle}=\textsf{width} * \textsf{length}`

`\textsf{Area of a semicircle}=\frac12 \pi r^2 \quad \textsf{(where r is the radius)}`

`\textsf{Diameter of a circle}=2r \quad \textsf{(where r is the radius)}`

Area of rectangle

Given dimensions of the rectangle:

• width = 7 cm
• length = 11 cm

Substituting these values into the formula:

`\implies \textsf{Area}=\textsf{7} * \textsf{11}=77\: \sf cm^2`

Area of semicircle

Diameter of semicircle = 11 - 2 - 2 = 7 cm

⇒ Radius (r) = 7 ÷ 2 = 3.5 cm

`\textsf{let}\: \pi=(22)/(7)`

`\implies \textsf{Area}=\frac12 \left((22)/(7)\right) (3.5)^2=19.25\: \sf cm^2`

Area of shaded region

= area of rectangle - area of semicircle

= 77 - 19.25

= 57.75

`\sf =57 \frac34 \:cm^2`