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Head First 2D Geometry by Dawn Griffiths, Stray

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organize your work in a table
Keep track of complex comparisons
with a table
There’s a whole bunch of stuff you’re working out to pick the
best hot tub. You need to keep track of side length and angles for
the carpenters, as well as butt-space to choose the best tub for the
band…and you need to know what calculation goes with which
tub! A table can help you make sure all that information is right at
your fingertips.
9.8m
Model Shape Polygon No sides Perimeter Butts Angles Side
length
Tri-tub
Chill-out-corner
Hex-it-up
7th Heaven
Relaxiv8
9 Sides
Magic Circle
= 19.6 butts
5.7m
Ev
erything you’v
e a
lr
eady
w
orked out can be nic
ely
organized in this table.
= 11.17m
butts
= 11.17
=
22.3 butts
0.5
296 Chapter 7
T
hese thr
ee might make y
our
brain hurt a bit—don’t panic,
w
e’ll ta
lk more about them l
ater.
regular polygons
Let’s look for some quick answers here!
Based on the work you’ve already done, you should already be able
to fill in all the boxes in this table except for the shaded ones.
Model Shape Polygon
Name
No sides Perimeter Butts Angles Side
length
Tri-tub
Chill-out-corner
Hex-it-up
7th Heaven
Relaxiv8
9 Sides
Magic Circle
you are here 4 297
T
ha
t’s the infini
ty
symbol!
Don’t w
orry if these made
y
our head hurt....
If you need help r
emember
ing these, check
out the “Nonagon” song by T
hey Might Be
Giants on YouT
ube. Goofy but genius.
Mor
e on these l
ater
in the chapter.
exercise solution
Let’s look for some quick answers here!
Based on the work you’ve already done, you should already be able
to fill in all the boxes in this table except for the shaded ones.
Model Shape Polygon No sides Perimeter Butts Angles Side
length
Tri-tub
Equilateral
Triangle
3
11.17m
22.3
60º
3.72m
Chill-out-corner
Square
4
9.8m
19.6
90º
2.45m
Hex-it-up
Hexagon
6
7th Heaven
Septagon
7
Relaxiv8
Octagon
8
9 Sides
Nonagon 9
Magic Circle
Circle
8.67m
17.3
Nearly
180º
Nearly 0
298 Chapter 7
regular polygons
You need to pick a hot tub fast! Write down ANYTHING you can think of
that could help you find the area of the 6-, 7-, 8-, and 9-sided tubs. No
idea is too crazy. If you run out of space grab some paper. Give yourself
at least 5 minutes, and then come and join our brainstorm results over on
the next page.…
Brain Storm
That’s a pretty table and all, but it looks like
you just ran straight into a DEAD END. Triangles,
squares, and circles are one thing but helloooo—area
of a septagon? We don’t have formulas for the areas
of any of those other shapes. And if we have to
work them out one by one this could take forever. By
tomorrow? Not gonna happen.
It’s a fair point.
On the surface it looks like most of our table is filled
in, but we’re still a long way from choosing that ideal
hot tub.
Time to change our strategy!
you are here 4 299
brain storm
Phone a f
r
i
end!
Brain Storm
W
e could chop the
oc
tagon int
o r
ectangles
and tr
iangles
We could try tha
t thing w
e did t
o
work out the p
izza area, where w
e
chopp
ed i
t up into tr
iangle-like slic
es.
So what might help us find the area of the 6-, 7-, 8-, and 9-sided tubs?
Here are the ideas we came up with, but you might have had different
ideas, or extra ideas we didn’t think of. The more, the merrier!
300 Chapter 7

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