two trapezoids make a parallelogram

Here are two congruent trapezoids. Draw them together so that

they form a single parallelogram.

Parallelogram width = trapezoid lower base + trapezoid upper base

The parallelogram is made up of two trapezoids. This means that the area of each trapezoid

must be half that of the parallelogram, and we know that the area of a parallelogram is equal to

height x width.

What’s the width of the parallelogram?

The trapezoid upper and lower bases added together.

What’s the height of the parallelogram?

The trapezoid height

What ideas do you have about how to calculate the area of a trapezoid?

Sp

in one of the

trap

ezoids 180˚ and

y

ou can fi

t them

both t

ogether to

f

orm a para

llelogram.

=

trapezoid height

Parallelogram height

Calculate trapezoid area using

base length and height

So what we’ve discovered is that, like with the other

shapes you’ve encountered so far, there’s a shortcut

we can take if we want to find the area of a trapezoid.

All we need to do is add together the upper and lower

base lengths, multiply by the height, and then divide

by two.

2

Trapezoid Area = height (base 1 + base 2)

264 Chapter 6

quadrilaterals

What’s the charge for maintaining the trapezoid lawn? Thankfully, Ed went back and collected

some extra measurements to help you out with the perimeter.

28 meters

25 meters

30 meters

24 meters

53 meters

you are here 4 265

exercise solution

What’s the charge for maintaining the trapezoid lawn? Thankfully, Ed went back and collected

some extra measurements to help you out with the perimeter.

24 meters

28 meters

53 meters

25 meters

30 meters

Trapezoid area = 1/2 x 24 x (28 + 53)

= 12 x 81

= 972 meters

2

Trapezoid perimeter = 28 + 30 + 53 + 25

= 136 meters

Maintenance charge = $0.05 x 972 + $0.10 x 136

= $48.60 + $13.60

= $62.20

266 Chapter 6

quadrilaterals

The Trapezoid Exposed

This week’s interview:

What’s So Special About Trapezoids?

Head First: Hey, Trapezoid, nice to have you on

the show tonight.

Trapezoid: It’s a real pleasure. I don’t seem to get

out as much as some of the other shapes.

Head First: What do you mean?

Trapezoid: Well, everyone knows about Square and

Rectangle, although they’re kind of boring if you

ask me. Kite gets good press because it looks like…

well…a kite. But me? Everyone forgets about me.

Head First: I notice that you didn’t mention

Parallelogram. Don’t you guys have something in

common?

Trapezoid: Some would say we’re family, and I

guess you could say we’re kinda like cousins. I have

only one pair of parallel sides, and Parallelogram

has two. But don’t you think that’s just being greedy?

Parallelogram’s just a lopsided, funny-looking

Rectangle if you ask me, and I don’t limit myself like

that.

Head First: But aren’t you just like Triangle but

with one of the points chopped off ?

Trapezoid: That’s one way you could talk about

me, yes, but the key thing is that I have one pair of

parallel sides, and Triangle doesn’t. Um, I wouldn’t

talk to Triangle about that, he’s still a bit sensitive.

Head First: But don’t you have one nice thing in

common with Triangle?

Trapezoid: You did your research, didn’t you?

We’ve all heard of an Isosceles Triangle, right? Well,

Trapezoids can be Isosceles, too.

Head First: What’s special about that?

Trapezoid: It’s still a Trapezoid, but with congruent

legs. And by legs I mean the sides that aren’t bases.

Isosceles Trapezoid is a bit more regular than me,

there’s more symmetry about him. He’s thinking

about getting into modeling, from what I hear. At the

very least, it must make shaving much easier.

Head First: What about diagonals?

Trapezoid: What about them? Sure, I have them,

but I can’t say much about them. Now Isosceles

Trapezoid, he has congruent diagonals, and he has

some congruent angles, too. Some guys have all the

luck.

Head First: Well, that’s all we have time for,

Trapezoid, thanks for stopping by.

A trapezoid is a four-sided shape

with one pair of parallel sides called

bases.

Since the bases are parallel, this

means that you have two pairs of

supplementary angles.

An isosceles trapezoid is a trapezoid

with congruent “legs.” The lower

base angles are congruent, the upper

base angles are congruent, and the

diagonals are congruent, too.

you are here 4 267

Start Free Trial

No credit card required