Head First 2D Geometry

trapezoids have only two parallel sides

262 Chapter 6

There are some familiar things about

this shape

It’s a four-sided shape, but it only has one pair of parallel sides.

These parallel sides are called bases. We call this shape a

trapezoid.

A trapezoid

has exactly one

pair of opposite

parallel sides.

But what’s the area?

In theory, we could split the trapezoid into a rectangle and two

right triangles, and then add together the area of each shape. The

trouble is, we don’t have enough information to do this. We know

that they’re both right triangles, but we don’t know what the other

two angles are, and we only know the length of one of the sides. So

what can we do instead?

The bases here

are parallel.

Since the bases are

parallel, the angles

here are supplementary

(remember your F, N,

and Z patterns?).

24 meters

28 meters

53 meters

24 meters

…but we can’t work out the

area of the triangles because

we don’t know enough side

lengths.

We can split the trapezoid

into simpler shapes…

you are here 4 263

quadrilaterals

Instead of splitting the shape up, let’s add to it and see if that

helps us figure out how to find the area of a trapezoid. Here are

two congruent trapezoids. Draw them together so that they form

a single parallelogram.

What’s the width of the parallelogram?

What’s the height of ...