Section 7 –5Areas of Regular Polygons

Objectives:To find the area of a regular polygon

Radius: Distance from the center to a vertex.Apothem: Perpendicular distance from center to a side.

Regular Polygons

Example 1 Finding Angle Measures

A) The figure below is a regular pentagon with radii and an apothem drawn. Find the measures of each numbered angle.

B) The figure below is a portion of a regular octagon. Find the measure of each numbered angle.

The radii divide regular polygons into congruent isosceles triangles. What formula could you use to find the area of each triangle?

𝑨=𝟏𝟐𝒂𝒔

Since there are “n” congruent triangles in each regular polygon, the Area of any regular polygon would be .

How do you find perimeter of a regular polygon?

P

So you can replace the n and s in the formula with P (for perimeter) so the formula for the area of

regular polygons becomes:

a is the APOTHEMp is the perimeter of the polygon

Area of Regular Polygons

𝑨=𝟏𝟐𝒂𝒑

Example 2 Finding the Area of a Regular Polygon

A) Find the area of a regular decagon with a 12.3 inch apothem and 8 in sides.

B) Find the area of a regular polygon with twenty 12-inch sides and a 37.9 in apothem.

Example 3 Finding the Area of a Regular Polygon (finding Apothem)

A) Find the area of the regular hexagon below.

B) Find the area of a regular hexagon with side lengths of 16 feet.

C) Find the area of the octagon below.

Example 4 Finding the Area of an Equilateral Triangle

A) Find the area of the equilateral triangle below.

B) Find the area of an equilateral triangle with apothem 8 cm. Leave your answer in simplest radical form.

C) Find the area of the equilateral triangle below.

Homework

• Textbook Page 382 – 384; #1 – 3, 10 – 18 Even, 36 – 38