&KDSWHU
10-2
Perimeter
Objective To use a formula to find the perimeter of a regular polygon • To find missing
dimensions given the perimeter of a polygon • To find the perimeter of a complex figure • To explore
how changing the dimensions of a polygon affects the perimeter
NASA’s Cassini spacecraft photographed an enormous hexagon
above Saturn’s north pole. If it were a regular hexagon, with each
side measuring about 12 500 km, what would its perimeter be?
The (P) of a polygon is the sum of its side lengths.
Let srepresent the length of one side of a regular hexagon.
Pss ssss 6 s
6(12,500) Substitute 12,500 for s.
75,000
So the perimeter of the hexagon would be 75 000 km.
perimeter
Nonsquare rectangles are notregular polygons
because all the sides are notthe same length.
Find the perimeter of a rectangle with a length
of 275.4 ft and a width of 102.3 ft.
P2(w)
2(275.4102.3) Substitute given values.
2(377.7) Simplify.
755.4
So the perimeter of the rectangle is 755.4 ft.
If you know the values of all but one variable in a formula,
you can use algebra to find the value of the unknown variable.
Key Concept
Perimeter of a Regular Polygon
Pns, where nis the number of sides and
sis the side length
Perimeter of a Rectangle
P 2 2 wor P2(w), where is the
length and wis the width
The perimeter of a regular octagon
is 128 inches. What is the length
of each side?
P 8 s
128 8 s Substitute for P.
Divide both sides by 8.
16 s Simplify.
Check:P 8 s
128 8(16)
128 128 Tr u e
So each side is 16 inches long.
?
8 s
8
128
8
A rectangle has a perimeter of 198 meters
and a length of 66.4 meters. What is its width?
P 2 2 w
198 2(66.4) 2 w Substitute for Pand .
198 132.8 2 w Multiply.
198 132.8132.8 132.8 2 w
65.2 2 w Simplify.
65.2 2 2 w 2 Divide both sides by 2.
32.6 w
Check:P 2 2 w
198 2(66.4) 2(32.6) 132.8 65.2
198 198 Tr u e
So the width is 32.6 meters.
?
Subtract 132.8
from both sides.