Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 14: Quadrilaterals 189

To find the area of parallelogram ABCD, it’s not enough to know that AB = 13 meters and BC =
10 meters. You could use either of those measurements as the base, but neither of them is a
height. You need to know the perpendicular distance between two bases. If you know that the
height, drawn to BC, is 12 meters, then you can find that the area is 12 v 10 or 120 square meters.

WORLDLY WISDOM

Remember that area is always measured in square units. That’s because you multiply

a length in units (such as inches, feet, or meters) by another length in the same units.

Units multiplied by units equals units squared, or square units.

That area formula of base times height (A = bh) will work for any parallelogram, including
rectangles, rhombuses, and squares. But there are other area formulas, specific to those special
parallelograms, which may be useful from time to time. Some are just another way of saying
things. Because a rectangle has adjacent sides that are perpendicular, the sides, usually called
the length and the width, are the base and the height, so you see the formula for the area of a
rectangle as A = L v W. The formula for the area of a square is special, because it is a rectangle,
so you could use A = L v W, but all four of its sides are the same length, so the formula becomes
A = s^2.

WORLDLY WISDOM

The habit of referring to the exponent 2 as “squared” comes from the fact that the

area of a square is the length of a side to the second power.

Let’s look at a story problem using area.

Suppose you want to buy carpet for a room that measures 15 feet by 20 feet. The room is a
rectangle, so you multiply 15 by 20 and go to the carpet store, knowing you need 300 square feet
of carpet. When you arrive, you find that carpet is sold by the square yard, not the square foot.
What now?

You have two choices. Your first option is to start over and figure out the measurements of your
room in yards instead of feet. You know there are 3 feet in a yard, so 15 ÷ 3 = 5 yards and 20 ÷ 3
= 6^2
3
yards. Then you can multiply 5 by 6^2
3
to find out you need 33^1
3
square yards.

Your second option is to take your 300 square feet and divide by the number of square feet in a
square yard. A square yard is a yard times a yard, or 3 feet times 3 feet, so it’s 9 square feet. Your
300 square feet divided by 9 is 33^1
3
square yards. In both cases, you arrived at the same answer.