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.

Explanation:

Step1: Calculate ceiling area

The ceiling is a rectangle with length $l = 13$ ft and width $w = 12$ ft. The area of a rectangle is $A = l\times w$. So, $A_{ceiling}=13\times12 = 156$ square - feet.

Step2: Calculate area of two walls with length - height dimensions

Two walls have dimensions length $l = 13$ ft and height $h = 8$ ft. The area of each of these walls is $A = l\times h$. The combined area of these two walls is $A_1 = 2\times(13\times8)=208$ square - feet.

Step3: Calculate area of two walls with width - height dimensions

Two walls have dimensions width $w = 12$ ft and height $h = 8$ ft. The area of each of these walls is $A = w\times h$. The combined area of these two walls is $A_2 = 2\times(12\times8)=192$ square - feet.

Step4: Calculate total surface area

The total surface area $A_{total}=A_{ceiling}+A_1 + A_2$. So, $A_{total}=156 + 208+192=556$ square - feet.

Answer:

556 square feet