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Head First 2D Geometry by Dawn Griffiths, Stray

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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 dont 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
Lets 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
Lets 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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