Answer:
[tex]A_{living\ room}=A_{rectangle}+A_{semi-circle}\\\\A_{living\ room}=lw+\frac{\pi r^2}{2}[/tex]
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:
[tex]A_{rectangle}=lw[/tex]
Where "l" is the length of the rectangle and "w" is the width.
The area of a circle can be calculated with this formula:
[tex]A_{circle}=\pi r^2[/tex]
Where "r" is the radius of the circle.
Therefore the following formula can be used to find the area of a semi-circle:
[tex]A_{semi-circle}=\frac{\pi r^2}{2}[/tex]
Where "r" is the radius.
Then, the area of the living room is:
[tex]A_{living\ room}=A_{rectangle}+A_{semi-circle}\\\\A_{living\ room}=lw+\frac{\pi r^2}{2}[/tex]
