Lesson: Areas of Regular Polygons Mathematics

In this lesson, we will learn how to find areas of regular polygons given their side lengths using a formula.

Lesson Plan

Students will be able to

derive and recall the formula for the area of a regular -sided polygon with side length : (note that this is equivalent to ),
calculate areas of -sided polygons given a side length or perimeter,
calculate side lengths and perimeters of regular polygons given their areas and number of sides,
calculate areas of compound shapes that are formed of regular polygons and other shapes.

Students should already be familiar with

right triangle trigonometry,
how to calculate the areas of triangles and various quadrilaterals (trapezoids, parallelograms, etc).

Students will not cover

Q1:

Find the area of a regular 14-sided polygon given the side length is 21 cm. Give the answer to two decimal places.

Q2:

The perimeter of a regular pentagon is 85 cm. Find the area giving the answer to the nearest square centimeter.

Q3:

Find the area of a regular hexagon with a side length of 35 cm giving the answer to two decimal places.