11.3 Areas of Regular Polygons &

Circles

Objectives =]

Learn how to find the area of polygons

& Find area of circles

Area of Regular Polygons

• In regular hexagon ABCDEF inscribed in circle G, GA and GF are radii, from the center of the circle to two vertices of the hexagon. GH is perpendicular to AF. This segment is called a Apothem.

APOTHEM::Definition::

A segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon.

To Find the Area• The area of a hexagon

is determined by adding the areas of the triangles.

• GH is perpendicular to AF, it is an altitude of AGF. a represents the length of GH and let s represent the length of a side of the hexagon.

• Area of triangle AGF ½ bh = 1/2 sa

The area of one triangle is (½)(side)(apothem) sq. units. So the area of the hexagon is 6(1/2 sa) sq. units. The perimeter of the hexagon is 6s units. You can substitute P for 6s in the area formula.

SOO instead of….

A = 6(1/2 sa) its… A = 1/2(Perimeter)(apothem)

**This formula can be used for any regular hexagon**

Ex. 1• Find the area of the pentagon with a

perimeter of 40 centimeters.

Ex. 2 Find the area of the Octagon. The apothem is 5

Area of a Circle

• If a circle has an area of A square units and a radius of r units than

A=pi.r squared

Ex. 3Find the area of the circle B if the diameter is 10.

round to nearest tenth.

ASSIGNMENT =]

Pg. 613:: # 8-22Pg 614:: # 30 & 31 , # 36 & 37Pg 615:: #40