Question

for the purpose of purchasing new baseboard and carpet, complete parts a and b below.
a. find the area and perimeter of the room (neglecting doors).
b. identify whether baseboard has to do with area or perimeter and the same with carpet.
a. the area of the room is □ and the perimeter is □

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l = 10.5\) ft and \(w=8\) ft.
\(A=10.5\times8 = 84\) square feet.

Step2: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is \(P = 2(l + w)\).
Substitute \(l = 10.5\) ft and \(w = 8\) ft into the formula:
\(P=2(10.5 + 8)=2\times18.5 = 37\) feet.

Step3: Determine the relation for base - board and carpet

Baseboard is installed along the edges of the room (the boundary), so it is related to the perimeter. Carpet covers the floor of the room, so it is related to the area.

Answer:

a. The area of the room is \(84\) square feet and the perimeter is \(37\) feet.
b. Baseboard has to do with perimeter. Carpet has to do with area.