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Head First 2D Geometry by Dawn Griffiths, Stray

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quadrilaterals
…and the customers keep flooding in
I’ve put a new garden
bed in the middle of my lawn
for a ton of colorful flowers.
There’s less lawn to mow, so
can I get a discount?
Another
cus
t
omer
30 meters
20 meters
4.5 meters
13 meters
T
hese sides ar
e congruent.
These sides ar
e congruent, t
oo.
Check out the sketch of the lawn. How would you calculate just
the area of the lawn, without the flower bed? Describe what you
need to do in words and sketches, and assume you have all the
measurements you need.
you are here 4 253
sharpen solution
=
-
That’s great, but
how do we find the area of
the flower bed? It’s not a
rectangle, and it doesn’t look
like a parallelogram either.
Area of lawn
Area of the main lawn rectangle Area of the
flower bed
=
-
OR
So to find the total area of the lawn we have to mow, we need to find the area of the lawn as
though the flower bed wasn’t there, and then subtract the area of the flower bed.
Check out the sketch of the lawn. How would you calculate just
the area of the lawn, without the flower bed? Describe what you
need to do in words and sketches, and assume you have all the
measurements you need.
True, it isn’t a rectangle or a parallelogram.
The opposite sides of the flower bed aren’t parallel. Could you
use a technique from earlier in this chapter to try to figure out
the area of that shape?
254 Chapter 6
quadrilaterals
Geometry Magnets
Arrange the triangles below to form the same shape as the flower
bed. Then see if you can rearrange them to form a rectangle. Whats
the base of this rectangle? What’s the height? What does this tell you
about how you might find the area of the flower bed?
Hint: you’ll need to flip some of the shapes over to get the rectangle.
you are here 4 255
kites have adjacent congruent sides
Geometry Magnets Solution
Rearrange the triangles below to form the same shape as the flower
bed. Then see if you can rearrange them to form a rectangle. Whats
the base of this rectangle? What’s the height? What does this tell you
about how you might find the area of the flower bed?
Hint: you’ll need to flip some of the shapes over to get the rectangle.
The rectangle is
half the height of
the flower bed.
The areas of the two shapes must be the same as they’re
made up of the same triangles. So we can find the area
of the flower bed by finding the area of the rectangle.
So if the shape
of the flower bed
isn’t a parallelogram,
what is it?
256 Chapter 6
Just what it looks like: it’s called a kite.
No crazy geometry jargon here! Like a parallelogram, a kite has four
sides. There’s one big difference though. A parallelogram has opposite
congruent sides, but a kite has two pairs of adjacent congruent sides.
The diagonals of a kite are important, too. A diagonal is a straight line
that connects one corner to the corner opposite. For a kite, these diagonals
are always perpendicular to each other.
T
hese sides
ar
e congruent.
T
hese sides ar
e
congruent, t
oo.
T
he diagonals of a ki
te
ar
e per
p
endicul
ar.
The rectangle and flower bed have the same width.

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