It’s a regular polygon, so the angles are equal = 720º = 120º

T

his is wha

t the carp

enter

needs t

o know.

regular polygons

But what about dimensions?

Phew! The only thing left on your to-do list is to tell the carpenters

what length each side of the hot tub is.

Hint—look back at page 293 if you’re not sure where to start....

The total area of the hot tub is 6 square meters. Use what

you know about the hexagon hot tub angles to find the length

of each side of the hot tub. (Hint: it helps if you split it into

those sector triangles!)

you are here 4 315

brain barbell solution

These 6 triangles are the same (congruent). Each one must have

an area of 1 square meter.

The angles in the middle add up to 360º, so this angle here must

be 60º.

Each internal angle is 120º—and we know the triangle is

ISOSCELES because the side lengths are both equal to the

circumradius of the polygon, so the other angles must both be

120º/2 = 60º.

Each 1 sq meter triangle is EQUILATERAL.

So we can use the equilateral triangle area formula!

The total area of the hot tub is 6 square meters. Use what

you know about the hexagon hot tub angles to find the length

of each side of the hot tub.

Solution

60º

60º

3t

2

4

3t

2

4

4

3

Area =

1m

2

=

= t

2

2.31 = t

2

1.52m = t

Length of each side.

t is side length.

An isosceles tr

iangle

has t

wo equa

l sides,

and t

wo equa

l angles.

Any tr

iangle wi

th

thr

ee 60º angles is

equil

a

tera

l.

Ar

ea of each

triangle is the t

otal

p

olygon area divided

by the number of

tr

iangles.

Use a ca

lcul

a

t

or!

316 Chapter 7

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