Page 136 - Math Course 1 (Book 2)

Geometric Area: Polygons and Circles

Mo. 10

Lesson 6 Area of a Circle

Words If a circle has an area of A square units
and a radius of r units, then the area is
KEY CONCEPTS: the product of π and the square of the
1. Find areas of regular polygons. radius.
2. Find areas of circles.
r
Symbols A = πr 2

MO. 10 - L6a

Finding Areas of Polygons

and Circles

Vocabulary A-Z Let’s Begin
Let us learn some vocabulary

Area of a Regular Polygon
apothem
A segment from the center of the regular polygon Example
perpendicular to a side of the polygon.

C D Find the area of a regular pentagon with a
perimeter of 90 meters.

B
B E

Q
A C
G
A F

J
E F D
H G

Key Concept Apothem: The central angles of a regular penta-

gon are all congruent. Therefore, the
360
measure of each angle is or 72
Area of a Regular Polygon 5
GF is an apothem of pentagon
Words If a regular polygon has an area of A ABCDE. It bisects ∠EGD and is a
square units, a perimeter of P units,
and an apothem of a units, then the perpendicular bisector of ED. So,
1
area is one-half the product of the m∠DGF = (72) or 36. Since the
perimeter and the apothem. 2
perimeter is 90 meters, each side is
1
Symbols A = Pa
2 18 meters and FD = 9 meters.

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