Applied Geometry
Lesson: 10 – 5
Areas of Regular Polygons
Objective:
Learn to find the areas of regular polygons.
Polygons
Center – A point in the interior of every
polygon that is equidistant from all the
vertices.
Apothem – A segment drawn from the
center perpendicular to the side of a
regular polygon.
Area of a
Regular Polygon
If a regular polygon has an area of A
square units, an apothem of a units, and
a perimeter of P units, then
Find the area of the regular polygon.
1
A  aP
2
1
A  (10.9)(72)
2
A  392.4in
2
The game has a hexagon
shaped board. Find its area.
1
A  aP
2
1
A  (7.8)(54)
2
A  210.6 in
2
Find the area of the shaded
region in the regular figure.
Area of Pentagon
Area of triangle
1
A  (5.5)( 40)
2
A  110
1
A  (8)(5.5)
2
A  22
Area of shaded region
Pentagon - Triangle
A  110  22
2
A  88 ft
Find the area of the shaded
region of the regular figure.
Area of Octagon
Area of Trapezoid
1
A  (2.4)(16)
2
A  19.2
1
A  (1.4)( 2  4.8)
2
A  4.76
Area of shaded region
Octagon – Trapezoid.
A  19.2  4.76  14.44 m
2
Significant digits
Precision in a measurement is usually
expressed by the number of significant
digits reported.
Significant digits
Nonzero digits are always significant
In whole numbers, zeros are significant if they
fall between nonzero digits.
In decimal numbers greater than or equal to 1,
every digit is significant.
In decimal numbers less than 1, the first
nonzero digit and every digit to the right are
significant.
Determine the number of significant digits.
779,000 mi
3 significant digits
Look at rule for whole numbers.
50,008 ft
5 significant digits
Look at rule for whole numbers
430.008 m
6 significant digits
Look at rule of decimals > 1
0.00750 cm
3 significant digits
Look at rule of decimals < 1
230.004500
9 significant digits
Look at rule of decimals > 1
Homework
Pg. 428 2 – 6 all, 8 – 22 E

Don’t do #1 & 3