quadrilaterals

Business is booming!

Her

e are a bunch of the

new l

awns your cus

t

omer

s

want t

o pay y

ou t

o mow.

Nice work, but that’s a lot

of time you’re gonna spend in

the office calcuating costs,

isn’t it?

Before too long, lots of new customers come flocking to the business.

Fair enough.

You can’t bill customers if you don’t have time to actually mow

their lawns. There is probably a way to speed things up a bit.…

Look again at the rectangle and triangles that make up a parallelogram.

What do you think you can do to speed up your calculations?

you are here 4 241

study hall conversation

So how can we speed

up the area calculation

for a parallelogram?

Jim

Jim: Well, a parallelogram is basically made up of just three

shapes, a rectangle and two triangles.

Frank: Yeah, but those two triangles look the same, right? So

maybe they’re congruent.…

Joe: Nice! So we could calculate one triangle area, multiply by

two, and then add on the area of the rectangle.

Jim: That’s still a few calculations per lawn, duh!

Frank: True. So I wonder if we could take it any further?

Joe: Maybe we can move these shapes around a bit. Could

we turn them into just one shape whose area we know how to

calculate?

Frank

Joe

242 Chapter 6

quadrilaterals

Geometry Magnets

Let’s see if we can figure out a quicker way of calculating the

area of a parallelogram. First, arrange the shapes below to form

a parallelogram. Then, see if you can rearrange them to form a

rectangle. What does this tell you about a more general formula for

finding the area of any parallelogram?

you are here 4 243

parallelogram area is same as rectangle area

Geometry Magnets Solution

Let’s see if we can figure out a quicker way of calculating the

area of a parallelogram. First, arrange the shapes below to form

a parallelogram. Then, see if you can rearrange them to form a

rectangle. What does this tell you about a more general formula for

finding the area of any parallelogram?

Y

ou can make a para

llelogram and

a r

ec

tangle out of the same shap

es.

The areas of both the parallelogram and the rectangle must be the same because

they’re made up of the same shapes. So you can find the area of a parallelogram

by finding the area of a rectangle with the same base length and height.

244 Chapter 6

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