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

Answer:

$A_{living\ room}=A_{rectangle}+A_{semi-circle}\\\\A_{living\ room}=lw+\frac{\pi r^2}{2}$

Step-by-step 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:

$A_{semi-circle}=\frac{\pi r^2}{2}$

Where "r" is the radius.

Then, the area of the living room is:

$A_{living\ room}=A_{rectangle}+A_{semi-circle}\\\\A_{living\ room}=lw+\frac{\pi r^2}{2}$