Regular polygon areas

Regular polygon areas

By Marcia Davis

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.

Multiple Select

Which of these figures are regular polygons?

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 using the triangles method we just went over in the lesson:

area of pentagon = area of one triangle x 5

= 1/2 base x height x 5

= 1/2 x 6m x 4m x 5

= 12m² x 5 = ?

• 120m²

• 100m²

• 60m²

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

​

Area = 1/2 apothem x perimeter

​

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

Multiple Choice

Find the area of the regular polygon using the quicker method:

area = 1/2 apothem x perimeter

= 1/2 x 4m x (5 sides x 6m)

= 1/2 x 4m x 30m

= 1/2 x 120m² = ?

• 120m²

• 100m²

• 60m²