The area of the given figure is 38.13 in² and its perimeter is 23.42 in.
First, we will determine the area of the semicircle,
Area of a semicircle = Half area of a circle
Area of a circle = [tex]\pi r^{2}[/tex]
∴ Area of semicircle = [tex]\frac{1}{2}\pi r^{2}[/tex]
Where r is the radius
From the diagram, the base of the figure (length of the rectangle) equals the diameter of the semicircle
∴ diameter = 6 in.
But
[tex]radius = \frac{diameter}{2}[/tex]
∴ [tex]radius = \frac{6}{2}[/tex]
r = 3 in.
Now, from
Area of semicircle = [tex]\frac{1}{2}\pi r^{2}[/tex]
Area of the semicircle = [tex]\frac{1}{2} \times 3.14 \times 3^{2}[/tex]
Area of the semicircle = [tex]1.57 \times 9[/tex]
Area of the semicircle = 14.13 in².
For the rectangle,
Area of rectangle = [tex]length \times width[/tex]
Length = 6 in.
and the width = 4 in.
∴ Area of the rectangle = 6 × 4
Area of the rectangle = 24 in².
Now, for the area of the figure,
Area of the figure = Area of the semicircle + Area of the rectangle
∴ Area of the figure = 14.13 in². + 24 in².
Area of the figure = 38.13 in².
For the perimeter of the figure,
Perimeter is sum of all sides
∴ Perimeter of the figure = Width of rectangle + Length of rectangle + Width of rectangle + length of the half circumference
First, we will determine the length of the half circumference,
Length of the half circumference = [tex]\frac{1}{2}\times2\pi r = \pi r[/tex]
Length of the half circumference = 3.14 × 3
Length of the half circumference = 9.42 in.
From
Perimeter of the figure = Width of rectangle + Length of rectangle + Width of rectangle + length of the half circumference
∴ Perimeter of the figure = 4 in. + 6 in. + 4 in. + 9.42 in.
Perimeter of the figure = 23.42 in.
Hence, the area of the figure is 38.13 in² and its perimeter is 23.42 in.
Learn more here: https://brainly.com/question/21137908
