Head First 2D Geometry

Since the bases ar

e

para

llel, the angles

her

e are supplementary

…but w

e can’t w

ork out the

ar

ea of the tr

iangles because

we don’t know enough side

lengths.

int

o simpler s

hap

es…

trapezoids have only two parallel sides

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.

T

he bases her

e

(r

emember y

our F, N,

and Z pa

tterns?).

are para

llel.

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?

28 meters

A trapezoid

has exactly one

pair of opposite

parallel sides.

24 meters

53 meters

24 meters

W

e can spli

t the trapezoid

262 Chapter 6

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 the parallelogram?

What ideas does this give you about how to calculate the area of a trapezoid?

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