(Hint: i
t look
s a lot like one of the intermedia
te
stages of the circle ar
ea f
ormul
a!)
Combine these.
Base
Height
f
ormul
a w
e had f
or circle area:
1/2 x circumfer
ence x radius?
r
eminder if y
ou’re f
u
zzy.
polygon formula magnets solution
Polygon Formula Magnets Solution
Rearrange the magnets to find the general formulas for the perimeter
and area of our polygon hot tubs. Use each magnet exactly once.
Area of one triangle ‘sector’ =
Using 1/2 base x height
×
1/2
apothem
side length
×
×
number of sides
number of sides
apothem
apothem
side length
perimeter
1/2
1/2
side length
Y
ou can substi
tute perimeter
f
or side length x sides.
Total area =
Perimeter =
Total area =
×
×
Doesn’t this look like the intermedia
te
Don’t worry if you put the magnets in each
equation in a different order—because it’s all
multiplication the order isn’t important.
See page 230 f
or a
The apothem joins the center to the
middle of a side, bisecting it.
The apothem meets the side at a
right angle.
The circumradius joins the center to
a vertex.
The circumradius bisects the
internal angle.
308 Chapter 7