Question

Kevin wants to measure the area of his living room. The living room is a rectangle with a semi-circular alcove. What is the area of the room? Use 3.14 for π. A. 201.87 ft2 B. 225.42 ft2 C. 230.13 ft2 D. 244.26 ft2

Answer 1

`A_(living\ room)=A_(rectangle)+A_(semi-circle)\\\\A_(living\ room)=lw+(\pi r^2)/(2)`

Explanation:

You did not provide the dimensions of the living room, so I will give you a general explanation of the procedure you need to apply to solve the exercise:

According to the information provided in the exercise, the living room is a rectangle with a semi-circular alcove, then, you can conclude that its area can be obtained by adding the area of the rectangle and the semi-circle.

The area of a rectangle can be calculated with the following formula:

`A_(rectangle)=lw`

Where "l" is the length of the rectangle and "w" is the width.

The area of a circle can be calculated with this formula:

`A_(circle)=\pi r^2`

Where "r" is the radius of the circle.

Therefore the following formula can be used to find the area of a semi-circle:

`A_(semi-circle)=(\pi r^2)/(2)`

Where "r" is the radius.

Then, the area of the living room is:

`A_(living\ room)=A_(rectangle)+A_(semi-circle)\\\\A_(living\ room)=lw+(\pi r^2)/(2)`