Question

A.Find the total and area of the compound figures

B.Find the total perimeter of the compound figures

Answer 1

(a) The total area of compound figure is
`284.52ft^2`.

(b) The total perimeter of compound figure is 68.84 ft.

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 =
`(12ft)/(2) = 6 ft`

Part (a):

Now calculating the total area of the compound figure.

`\text{Total area}=\text{Area of rectangular figure}+(1)/(2)* \text{Area of circle}\\\\\text{Total area}=\text{Length}* \text{Breadth}+(1)/(2)* \pi r^2`

Now putting all the given values in this formula, we get:

`\text{Total area}=(19ft* 12ft)+(1)/(2)* 3.14* (6ft)^2\\\\\text{Total area}=284.52ft^2`

Part (b):

Now calculating the total perimeter of the compound figure.

`\text{Total perimeter}=2* \text{Length}+Breadth+((1)/(2)* \text{Circumference})\\\\\text{Total perimeter}=2* \text{Length}+Breadth+((1)/(2)* 2* \pi * r)`

Now putting all the given values in this formula, we get:

`\text{Total perimeter}=2* \text{Length}+Breadth+((1)/(2)* 2* \pi * r)\\\\\text{Total perimeter}=2* 19ft+12ft+((1)/(2)* 2* 3.14 * 6ft)\\\\\text{Total perimeter}=68.84ft`