 Given a regular polygon, you can find its area by dividing the polygon into congruent, non- overlapping, equilateral triangles.

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Presentation transcript:

 Given a regular polygon, you can find its area by dividing the polygon into congruent, non- overlapping, equilateral triangles.

Here a pentagon is separated into 5 congruent, non-overlapping, equilateral triangles.

 In order to determine the area of this pentagon, simply determine the area of one triangle, and multiply that number by 5.

Altitude of a triangle. 3.44

 If you have a regular polygon with n sides, you can still divide this polygon into n congruent, non- overlapping, equilateral triangles.

 The area of any regular polygon can be given by the following formula.

Here, a represents the apothem of the polygon, and p represents the perimeter of the polygon.

 An apothem of a polygon is the altitude of a triangle from the center of the polygon to a side of the polygon.

Apothem 3.44

√3 Determine the area of this hexagon.

√3

Substitute in values and simplify Area of the hexagon

Determine the area of this heptagon.

8

 The area of the polygon in practice problem 1 is approximately 48 square units.  The area of the polygon in practice problem 2 is approximately 194 square units.