Transcript Slide 1 - NEHSMath

Section 7-5 Areas of Regular Polygons
SPI 21B: solve equations to find length, width, perimeter and area
SPI 32L: determine the area of indicated regions involving figures
SPI 41A: determine the perimeter & area of 3 or 4 sided plane figures
Objectives:
• find area of a regular polygon
Regular Polygon:
• equilateral and equiangular
Parts of Regular Polygons
• Circle is circumscribed about the polygon
• Radius:
- distance from center to vertex
- divides figure into n congruent isosceles triangles
• Apothem: perpendicular distance from the center to the
side of polygon
Finding Angle Measures of Regular Polygons
The figure at the right is a regular
polygon. Find the measure of each
numbered angle.
m1 = 360 = 72
5
Divide 360 by # of angles
m2 = ½ m1 = 36
m3 = 180 – (90 + 36)
= 54
Area of a Regular Polygon
Regular Polygon: all sides and angles are 
Radii: divides the figure into  isosceles ∆
Area of Triangle = ½ bh or ½ as
There are n  sides and triangles, so:
• Area of n-gon = n ∙ ½ as or ½ ans
• Perimeter (p) = ns
• Using substitution:
A = ½ ap
Find Area of a Regular Polygon
Find the area of a regular decagon
with 12.3 apothem and 8 in sides.
1. Find the perimeter:
p = ns
= (10)(8)
= 80 in
2. Use formula for area of regular polygon:
A = ½ ap
= ½ (12.3)(80)
= 492 in2
Real-world and Regular Polygons
Some boats used for racing
have bodies made of a
honeycomb of regular hexagonal prisms
sandwiched between layers of outer
material. At the right is one of those
cells. Find its area.
The radii form six 60 degree s at the center. Use 30-6090 triangle to find apothem.
long leg = short ∙ 3
1. Find apothem:
a = 53
2. Find perimeter:
p = ns
= (6)(10)
= 60
3. Find Area
A = ½ ap
= ½ (53)(60)
 259.8 mm2
Practice
1. Find the area of a regular pentagon with 11.6 cm sides
and an 8-cm apothem.
P = ns
Area = ½ ap
p = (5)(11.6) = 58
A = ½ (8)(58) = 232 cm2
2. The side of a regular hexagon is 16 ft. Find the area.
a = 83 (30-60-90 triangle)
p = ns = (6)(16) = 96
A = ½ ap = ½ (83)(96) = 3843