Head First 2D Geometry

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regular polygons

If there were only two tub designs your work would be pretty much done,

but there are another five shapes of hot tub to compare in order to find the

perfect hot tub for that backstage area at the rock festival.

Two tubs down, five to go

Let’s take

the triangle

hot tub next.

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Tri-cuzi Chill-out-corner Hex-it-up 7th Heaven Relaxiv8 9 sides Magic Circle

Tubs can be any size, all depths 0.5m

19.6

17.3

Congruence

Pythagorean

Theorem

N, Z, and

F angles

Area =

1/2 base x

height

Hero’s

formula

Let’s work on the triangle tub next. You need to work

backward from area to find side length. Which tool from

your Geometry Toolbox is the best one for this job?

hero’s formula to the rescue

290 Chapter 7

Both of these deal

with triangle area.

Let’s work on the triangle tub next. You need to work

backward from area to find side length. Which tool from

your Geometry Toolbox is the best one for this job?

Solution

Hero’s formula is A = s(s-a)(s-b)(s-c).

It finds area in terms of the sides of the

triangle, so it’s a good fit with our problem:

finding perimeter from area.

You can use this formula but

you have to do quite a lot

of gnarly algebra to get to

the sides. Not our favorite

way to spend time....

All your toolbox tools ...