Head First 2D Geometry

you are here 4 293

regular polygons

You’ve found the formula for the area of an equilateral triangle

Recognizing special shapes is a great shortcut. Being able to spot

that a quadrilateral is a square, or that a triangle is an equilateral

triangle can save you a lot of work by letting you use extra tools

and formulas which apply to that special shape specifically.

Sides

Angles

Area

Longest must be shorter than

other two sides added together

Add up to 180º

1/2 base × height

or Hero’s formula

Are equal lengths

Are all 60º

= 3 t

2

4

Use your new equilateral triangle area formula to find the butt

count of the triangular-shaped hot tub.

Any old triangle Equilateral triangle

Just try

drawing a

triangle that

breaks this

rule!

294 Chapter 7

sharpen solution

Use your new equilateral triangle area formula to find the butt-

count of the triangular shaped hot tub.

3t

2

4

3t

2

4

Area =

Perimeter = 3t

= 3 x 3.72

= 11.17m

Butts = 11.17 = 22.3 butts

0.5

6 =

24 = t

2

3

3.72m = t

Length of

each side

Q:

Why bother learning another

formula? Won’t I be covered if I just

know Hero’s formula and the “1/2 base

× height” version?

A: Any time you use Hero’s formula

to work on a equilateral triangle you’re

gonna wind up doing all the math we just

did anyway. If you can learn the equilateral

triangle area formula then you won’t ...