Section 7 –5 Areas of Regular Polygons Objectives: To find the area of a regular polygon

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

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 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 The radii divide regular polygons into congruent isosceles triangles. What formula could you use to find the area of each triangle? 𝑨= 𝟏 𝟐 𝒂𝒔 Since there are “n” congruent triangles in each regular polygon, the Area of any regular polygon would be 𝑨=𝒏∙ 𝟏 𝟐 𝒂𝒔.

P =𝒏∙𝒔 𝑨= 𝟏 𝟐 𝒂𝒑 How do you find perimeter of a regular polygon? So you can replace the n and s in the formula 𝑨=𝒏∙ 𝟏 𝟐 𝒂𝒔 with P (for perimeter) so the formula for the area of regular polygons becomes: 𝑨= 𝟏 𝟐 𝒂𝒑

Area of Regular Polygons 𝑨= 𝟏 𝟐 𝒂𝒑 a is the APOTHEM p is the perimeter of the polygon

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 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