Area of Regular Polygons

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.

Multiple Choice

Which figure is a polygon?

Multiple Select

Which of these figures are regular polygons?

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 from each vertex into the center

• The vertex is where 2 line segments meet.

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

Multiple Choice

Which of these regular polygons have congruent triangles in them?

Multiple Choice

How do you make a congruent triangles in a regular polygon?

• Draw a line from one side to the other.

• Draw a line from a vertex to a vertex.

• Draw line from the vertex to the center.

• Draw a square.

Step 2:Find the area of one triangle.

• Remember A=1/2BH

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

Multiple Choice

What is the area of the triangle that has a 4in base and 10 in height?

• 40in

• 40 in²

• 20 in²

• 14in²

Multiple Choice

What is the area of a triangle that has a base of 12 ft and a height of 14ft?

• 42 ft²

• 84ft²

• 168ft²

• 13 ft²

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.

Multiple Choice

What is the area of the triangle in this polygon?

• 56cm²

• 7.5cm²

• 28cm²

Multiple Choice

How many sides does this figure have?

• 3

• 4

• 6

• 8

Multiple Choice

If the area of the triangle in this figure is 28cm², what is the area of the whole figure?

• 120cm²

• 168 cm²

• 280 cm²

Multiple Choice

Find the area of the regular polygon.

• 120m²

• 100m²

• 60m²