188 Part 3: The Shape of the World
Perimeter of Quadrilaterals
It’s easy to calculate the perimeter of quadrilaterals. Just as with triangles, you simply add up the
lengths of the sides. Most figures don’t even have a special formula for perimeter.
For a rectangle, you see the formula P = 2L + 2W. Because the opposite sides are the same length,
you have two of the lengths and two of the widths. For a square or a rhombus, that becomes P = 4s.
All the sides are the same length, and you have four of them.
Let’s look at a story problem using perimeter.
Suppose Marianna wants to build a fence around her vegetable garden. If the garden is a rect-
angle 30 feet long and 15 feet wide, and fencing costs $1.25 per foot, how much will it cost to
fence the garden?
The perimeter of a rectangle is P = 2L + 2W, so she will need (2 v 30) + (2 v 15) = 60 + 30, or
90 feet of fencing. 90 feet of fencing at $1.25 per foot will cost 90 v 1.25 = $112.50. Marianna’s
fence will cost $112.50.Area of Quadrilaterals
The area of a quadrilateral is a little trickier to calculate than the perimeter, but once you know
a few formulas, it’s not hard at all. The area of any parallelogram is found by multiplying the
base times the height (A = bh). In a triangle, the height must be measured as the perpendicular
distance between a vertex and the base. In a parallelogram, the height is the perpendicular
distance between two bases.MATH TRAP
Don’t confuse the side with the height. In most parallelograms, the sides are not
perpendicular, so you can’t use a side as a height. The exception, of course, is
rectangles, where the sides do meet at right angles.AD13 1210BC