Hey all. Zaher wrote in with this practice problem while back, and I thought it’d make a good post, so here it is:
A room is 24 feet long, 18 feet wide, and 9 feet high. How many square yards of wallpaper are needed to paper the four walls of the room?
You got your basic area problem, right? How do I know it’s “area”? Well, area is the space on the surface of something. Like, how much carpet covers a floor, or how many tiles on a bathroom wall. Or paint on a room. If you’re covering a surface, you’re talkin’ area. Now, how to solve it?
You got a few bumps in the road. First, you got dimensions in feet, an’ you want an answer in yards. Whenever you got different measurements in a problem, I recommend always changin’ everything to the dimensions you want in yo’ answer first off. That means, changin’ all the feet to yards. Now, there’s three feet in a yard, and dat’s jus’ somethin’ you got to know. So, to change feet into yards, divide by 3.
24 feet = 8 yards
18 feet = 6 yards
9 feet = 3 yards
Hey, you gotta know you’re on the right track when all the numbers divide out evenly! Too bad real life don’t work dat way. ‘k. So’s, now it’s important to picture what the question’s about, specially with this kinda dimension question. You got a room, 8 yards by 6 yards, and 3 yards tall.
What’s the area of the 4 walls? That’s the real question… a wallpaper or carpet or tile (or anything that goes on a flat surface) question is an area question.
So… each wall got the same height, the height of the room…3 yards (9 feet):
wall 1: 3 yards × ?
wall 2: 3 yards × ?
wall 3: 3 yards × ?
wall 4: 3 yards × ?
So, what’s the width of the walls? well, 2 walls is 8 yards long (the two walls opposite of each other on the sides of the room that’re 24 feet) and 2 walls is 6 yards long (the two walls opposite of each other on the sides of the room that’re 18 feet).
wall 1: 3 yards × 8 yards
wall 2: 3 yards × 8 yards
wall 3: 3 yards × 6 yards
wall 4: 3 yards × 6 yards
To find the area, multiply:
wall 1: 3 yards × 8 yards = 24 square yards
wall 2: 3 yards × 8 yards = 24 square yards
wall 3: 3 yards × 6 yards = 18 square yards
wall 4: 3 yards × 6 yards = 18 square yards
And to find the total, add:
24 + 24 + 18 + 18 = 48 + 36 = 84 square yards
Answer’s 84!
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