Find area of the shaded portion of the figure

Question

asked Nov 22, 2023 68.6k views

1 Answer

Luka Kvavilashvili · Answer 1 · 2023-11-27T13:01:47+0000

Answer:

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

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:

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

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