The distance around any flat (two-dimensional) object is the object's perimeter. You can measure perimeter in linear units like meters, yards, centimeters or miles. If you are out for a drive through Platt National Park, for example, you might measure perimeter in miles as you drive along the park's Perimeter Road.

## Formula for Perimeter

To find the perimeter of any quadrilateral, add the lengths of its four sides. Let P = perimeter and s(n) = a measured side. The formula for any quadrilateral is:

P = s(1) + s(2) + s(3) + s(4)

What is the perimeter of a rhombus with sides 444 mm long?

[insert drawing rhombus w/ labelled sides 444 mm]

• P = 444 mm + 444 mm + 444 mm + 444 mm
• P = 1,776 mm

That's a patriotic rhombus! Here is an irregular quadrilateral. What is its perimeter?

[insert drawing irregular quadrilateral sides 5 yards, 7 yards, 9 yards, 11 yards]

• P = 5 yds + 7 yds + 9 yds + 11 yds
• P = 32 yds

## Kite

What is the perimeter of this kite?

[insert labelled drawing with kite with two sides = 43 cm, two sides = 71 cm]

• P = 43 cm + 43 cm + 71 cm + 71 cm

A kite has two pairs of congruent sides. If you labelled one of the short, paired sides as a and the longer, paired side as b, the formula would be:

• P = 2(a) + 2(b)

OR

• P = 2(a + b)

## Unknown Side

What can you do if you do not know the measurement of all four sides of a quadrilateral?

For certain quadrilaterals, if you have three measured sides, you can find the measure of the unknown side. For several types of quadrilaterals, opposite sides are equal. If you know the measure of one side, you know the length of its opposite twin.

So, for these, P = perimeter, w = width and l = length (not height):

• P = 2(w) + 2(l)

OR

• P = 2(w + l)

The perimeter of these four quadrilaterals can be found using this technique:

1. Squares
2. Rhombuses
3. Rectangles
4. Parallelograms

If you have an irregular quadrilateral with an unknown side, you must either know the other three sides and the total perimeter, or you must physically measure the unknown side.

If you know the total perimeter and the measure of three sides, add the three known sides and subtract them from the perimeter to find the unknown length:

• P - (s(1) + s(2) + s(3)) = s(4)

Architects struggle constantly with irregular polygons. Empty lots may be strange shapes, but the architect still has to create houses on them:

[Insert copyright-free version floor plan of Octagon House available through Library of Congress at http://www.loc.gov/pictures/item/95860833/]

Here is a floor plan for your Math Club's new headquarters, squeezed onto an irregular plot of land next to the Sports Club's pavilion. The sides measure 13', 22', 24' and 14'. What is its perimeter?

Primeter of 73 feet? We sure hope so!

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Instructor: Malcolm M.
Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

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