Answer:
(a) The total area of compound figure is [tex]284.52ft^2[/tex].
(b) The total perimeter of compound figure is 68.84 ft.
Step-by-step explanation:
Perimeter: The total distance covered by the figure.
Area: It is defined as the space occupied by the figure.
Given:
Length of rectangular figure = 19 ft
Breadth of rectangular figure = 12 ft
Radius of circle, r = [tex]\frac{12ft}{2} = 6 ft[/tex]
Part (a):
Now calculating the total area of the compound figure.
[tex]\text{Total area}=\text{Area of rectangular figure}+\frac{1}{2}\times \text{Area of circle}\\\\\text{Total area}=\text{Length}\times \text{Breadth}+\frac{1}{2}\times \pi r^2[/tex]
Now putting all the given values in this formula, we get:
[tex]\text{Total area}=(19ft\times 12ft)+\frac{1}{2}\times 3.14\times (6ft)^2\\\\\text{Total area}=284.52ft^2[/tex]
Part (b):
Now calculating the total perimeter of the compound figure.
[tex]\text{Total perimeter}=2\times \text{Length}+Breadth+(\frac{1}{2}\times \text{Circumference})\\\\\text{Total perimeter}=2\times \text{Length}+Breadth+(\frac{1}{2}\times 2\times \pi \times r)[/tex]
Now putting all the given values in this formula, we get:
[tex]\text{Total perimeter}=2\times \text{Length}+Breadth+(\frac{1}{2}\times 2\times \pi \times r)\\\\\text{Total perimeter}=2\times 19ft+12ft+(\frac{1}{2}\times 2\times 3.14 \times 6ft)\\\\\text{Total perimeter}=68.84ft[/tex]
