Idiot\'s Guides Basic Math and Pre-Algebra

190 Part 3: The Shape of the World

MATH TRAP

To get units squared, you need to multiply units by units, that is, feet times feet or

meters times meters. But if you don’t pay attention to whether the units match, you

could be multiplying feet times inches, and that doesn’t give you square feet or square

inches. It just gives you the wrong answer. Make sure your units match.

The rhombus is usually thought of as the most unusual parallelogram, and its area formula is

the most different from the others. It’s built from the fact that the diagonals divide the rhombus

into four congruent right triangles. The area of each right triangle is one-half of the product

of its base and height, and it’s a right triangle, so the legs are the base and height. Each leg is

half of a diagonal, so if we call the the diagonals d 1 and d 2 , the area of each right triangle is

1

2

1

2

1

2

1

12 12 8

dd dd. Since there are four triangles that make up the rhombus, the area of the

rhombus is 4 1

8

1

122 12

 dd dd, or one-half the product of the diagonals.

How would you use that formula? Suppose you need to find the area of a rhombus with diagonals

12 cm and 20 cm. You could go through a lot of calculating to try to find the length of the side,

but you’d still need the height. Instead, remember that the area of a rhombus is half the product

of the diagonals. The area of the rhombus is^1

2

12 20 120 5 cm^2.

So you can use the formula A = bh for all parallelograms if you know the base and the height.

That covers the A = LW for the rectangle and the A = s^2 for the square. You can use the fancy

formula for the rhombus if you know the lengths of the diagonals. But what about a trapezoid?

It’s not a parallelogram, so your parallelogram formula doesn’t work, but you might need to

find its area anyway. How?

Well, it just so happens that if you draw the median of a trapezoid and cut along the median, you

can f lip the top piece over and set it next to the bottom piece. When you do that, the two pieces

will fit together to make a parallelogram.

(^1) d 2
2
(^1) d 2
2
(^1) d 1
2
(^1) d 1
2