Section 7 –5 Areas of Regular Polygons Objectives: To find the area of a regular polygon
Feb 23, 2016
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=𝟏𝟐 𝒂𝒔
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=𝟏𝟐 𝒂𝒑
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