Area of a Regular Polygon

Objective: Students will be able to identify regular polygons and find the area using congruent triangles.

What is a polygon?

• Straight sided, flat shapes that are closed

• Comes from the Greek word meaning “many angles”

What is a Regular Polygon?

• all sides are the same lengths (congruent)and all angles have the same measurements.

How can you find the area of a regular polygon?

• Divide the polygon into congruent triangles

• The number of triangles will be the same as the number of sides.

Step 1: Make congruent triangles

• Draw a line from each vertex to the center

• The vertex is where 2 line segments meet (corners)

• Make a dot in the center of the figure and connect it to each vertex.

Step 2:Find the area of one triangle.

• Remember A=1/2BH

• Don't forget to multiply by half or divide by 2.

Step 3: Find the area of the regular polygon

• Take the area you found from 1 congruent triangle and multiply it by the number of sides.

​Another, quicker, way to do this is to use the following formula:

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Area = 1/2 apothem x perimeter

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where the "apothem" is the connection from the center to the middle of a side (the height of one of the triangles​)