Question

in this section, youll solve problems involving surface area and perimeter.
you plan to set up a room in your basement for video streaming. the room needs proper lighting, good sound quality, and an appealing appearance for your audience.
your first task is to paint the four walls and the ceiling of the room. to determine how much paint to buy, you must calculate the surface area of the four walls and the ceiling.
the room has the following dimensions:
width: 12 ft.
length: 13 ft.
height: 8 ft.
whats the total surface area of the four walls and the ceiling?
ignore any windows or doors.
712 ft.²
356 ft.²
1,248 ft.²
556 ft.²

Explanation:

Step1: Calculate ceiling area

Ceiling area = length × width. Given length = 13 ft and width = 12 ft, so ceiling area \(A_{c}=13\times12 = 156\) \(ft^{2}\)

Step2: Calculate wall areas

There are two pairs of walls. One pair has dimensions length × height and the other has width × height.
Area of walls \(A_{w}=2\times(13\times8 + 12\times8)\)
First, calculate inside the parentheses: \(13\times8=104\) and \(12\times8 = 96\), then \(104 + 96=200\)
So \(A_{w}=2\times200=400\) \(ft^{2}\)

Step3: Calculate total area

Total area \(A = A_{c}+A_{w}\)
Substitute values: \(A=156 + 400=556\) \(ft^{2}\)

Answer:

556 \(ft^{2}\) (the fourth option)