Answer:
[tex]\sf C) \quad 57 \frac34 \:cm^2[/tex]
Step-by-step explanation:
To find the shaded area, subtract the area of the semicircle from the area of the rectangle.
Formulae
[tex]\textsf{Area of a rectangle}=\textsf{width} \times \textsf{length}[/tex]
[tex]\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Diameter of a circle}=2r \quad \textsf{(where r is the radius)}[/tex]
Area of rectangle
Given dimensions of the rectangle:
- width = 7 cm
- length = 11 cm
Substituting these values into the formula:
[tex]\implies \textsf{Area}=\textsf{7} \times \textsf{11}=77\: \sf cm^2[/tex]
Area of semicircle
Diameter of semicircle = 11 - 2 - 2 = 7 cm
⇒ Radius (r) = 7 ÷ 2 = 3.5 cm
[tex]\textsf{let}\: \pi=\dfrac{22}{7}[/tex]
[tex]\implies \textsf{Area}=\dfrac12 \left(\dfrac{22}{7}\right) (3.5)^2=19.25\: \sf cm^2[/tex]
Area of shaded region
= area of rectangle - area of semicircle
= 77 - 19.25
= 57.75
[tex]\sf =57 \frac34 \:cm^2[/tex]
