Area of Polygons

SECTION 5.03

After completing this lesson, you will be able to say:

I can use composition and decomposition to determine the area of polygons.

I can solve problems involving area of polygons using composition and decomposition.

Quadrilateral

What is a Polygon?

a plane figure with at least three straight sides and angles

Polygons

Polygons can be classified as regular or irregular.

Regular polygon:A polygon that has all congruent sides and angles.

Irregular polygon:A polygon that does not have all congruent sides and angles

Examples of Polygons

Regular Polygons

How can we decompose this hexagon to find the area?

The key to decomposing and composing polygons is to use only shapes you are familiar with. You would not want to decompose this hexagon into a shape you do not have the dimensions for or that you do not know how to solve for the area of.

Regular Polygons

To find the area using the decomposition of 12 congruent triangles, all you need to do is find the area of one of the right triangles and then multiply that by 12. Notice that the base of the triangle will be 5 inches because the triangle’s base is half of the hexagon’s side length.

Method 1

Regular Polygons

Method 2

Try It!

• Can you use the deconstruction method to find the area of this octagon?

Check your work

Irregular Polygons

How can we use decomposition to find the area of this irregular polygon?

Irregular Polygons

• Keep in mind there may be more than one way you can decompose an irregular polygon

• Here are two examples of how we can deconstruct this irregular polygon

Irregular Polygons

To calculate the area of this irregular polygon, all you need to do is calculate the area of each rectangle, then calculate the sum of the areas. Recall, the area of a rectangle A = l x w

Area of smaller rectangle 5 cm × 3 cm = 15 cm2

Area of larger rectangle 10 cm × 6 cm = 60 cm2

Total area of irregular polygon 15 cm2 + 60 cm2 = 75 cm2

Irregular Polygon

See if you can determine how to decompose this shape 

Irregular Polygons

You can see this irregular polygon is composed of one triangle and one rectangle.

The triangle has a base of 10 cm and a height of 3 cm. The height of the triangle was found by subtracting 9 from 12.

The rectangle has a length of 9 cm and a width of 8 cm.

Irregular Polygons

Try It!

Can you Calculate the area of the irregular polygon shown below.

Check your work

Check your work

Now that you completed this lesson, you should be able to say:

I can use composition and decomposition to determine the area of polygons.

I can solve problems involving area of polygons using composition and decomposition.