Question

Find area of the shaded portion of the figure ​

Answer 1

Answer:

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

Step-by-step explanation:

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

Formulae

$\textsf{Area of a rectangle}=\textsf{width} \times \textsf{length}$

$\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}$

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

Area of rectangle

Given dimensions of the rectangle:

• width = 7 cm
• length = 11 cm

Substituting these values into the formula:

$\implies \textsf{Area}=\textsf{7} \times \textsf{11}=77\: \sf cm^2$

Area of semicircle

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

⇒ Radius (r) = 7 ÷ 2 = 3.5 cm

$\textsf{let}\: \pi=\dfrac{22}{7}$

$\implies \textsf{Area}=\dfrac12 \left(\dfrac{22}{7}\right) (3.5)^2=19.25\: \sf cm^2$

Area of shaded region

= area of rectangle - area of semicircle

= 77 - 19.25

= 57.75

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