Head First 2D Geometry

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