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Head First 2D Geometry by Dawn Griffiths, Stray

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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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