Idiot\'s Guides Basic Math and Pre-Algebra

230 Part 3: The Shape of the World

Let’s take a look at one of these more interesting problems. The figure shown here is a

quadrilateral, but it’s definitely not part of the family of parallelograms. It’s called a concave

polygon. That dent from X to W to Y is where it caves in. Concave polygons cave in. Officially, a

polygon is concave if one of its diagonals falls outside the polygon. If you tried to draw a diagonal

from X to Y, it would be outside the quadrilateral.

DEFINITION

A concave polygon is one in which one or more diagonals falls outside the polygon. A

convex polygon is one in which all the diagonals fall inside the polygon.

All that is nice, but how do you find the area of something like that? You could divide and

conquer. Draw ZW and divide the figure into two triangles. Find the area of each and add them

together.

Of course, to find the area of each triangle, you need to know the lengths of a base and the height

to that base. If you knew that ZW = 4 cm and that an altitude from X to the extension of ZW

measures 3 cm, you could calculate the area of 'XWZ as^1

2

v 4 v 3 = 6 square centimeters. If the

altitude from Y is also 3 cm, you have the polygon broken into two triangles, and each triangle has

an area of 6 square centimeters, so the quadrilateral has an area of 12 square centimeters.

Z

W

XY

Z

4

5

X 33 VY

W