Finding paintable wall area and costing the paint

Four walls, minus a door and a window, then converted into tins and a price. The longest question on Exam 1, and the one where a shortcut saves the most time.

01 Worked Example Video

Every step of Finding paintable wall area and costing the paint explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Two windows

A room is 16 ft by 12 ft with 8 ft ceilings. There is one door 3 ft by 7 ft and two windows each 4 ft by 3 ft. Paint covers 150 ft² per gallon at $29.95.

What is the total cost of the paint? Type just the number.

Just the area

A room is 18 ft by 10 ft with 9 ft ceilings, one door 3 ft by 7 ft, and one window 60 in by 36 in.

How many square feet of wall are paintable? Type just the number.

Ceiling included

A room is 12 ft by 10 ft with 8 ft ceilings and one door 3 ft by 7 ft. The walls and the ceiling are painted.

How many square feet is that? Type just the number.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

$\text{wall area} = \text{perimeter} \times \text{height}$ one multiplication, not four rectangles

$\text{perimeter} = 2(L + W)$, then subtract each opening convert inches to feet BEFORE subtracting

Unroll the four walls into a single strip and the whole room becomes one rectangle: perimeter long, ceiling-height tall. Compute that once, cut out the door and windows, and you are done. The alternative — four separate rectangles — gives the same answer and takes four times as long.

Common slips

(1) Used area instead of perimeter. 14 × 11 is the floor, not the walls. You want 2(14 + 11). (2) Left the window in inches. 36 × 48 = 1,728 square inches, not square feet. Convert each side to feet first. (3) Included the ceiling or floor. Read what is being painted. (4) Rounded the tins down. Same ceiling rule as the coverage questions.

04 Practice — Step by Step

Unroll, subtract, cost

A room is 14 ft by 11 ft with 9 ft ceilings. It has one door, 3 ft by 7 ft, and one window, 36 in by 48 in. Paint covers 150 ft² per gallon and costs $34.50 a gallon.

Only the walls are painted. What will the paint cost?

Step 1

The wall area

Perimeter is 2(14 + 11) = 50 ft. Multiply by the 9 ft height.

Step 2

The window, in feet

36 in is 3 ft and 48 in is 4 ft. What is the window’s area in square feet?

Step 3

Paintable area

450 minus the door (21 ft²) minus the window.

Step 4

Gallons, then cost

417 ÷ 150 = 2.78. Round up, then multiply by $34.50.

Q11 Q13

Finding paintable wall area and costing the paint

Two minutes, four steps