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How to Find the Area of Irregular Polygons

How to Find the Area of Irregular Polygons
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  • 0:04 What's an Irregular Polygon?
  • 0:33 Area of an Irregular Polygon
  • 1:14 Example 1
  • 2:51 Example 2
  • 4:35 Lesson Summary
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Lesson Transcript
Instructor: Cassandra Cook

Cassandra Cook has taught grades K-8 and has a Specialist degree in Curriculum and Instruction

In this lesson we will learn the definition of an irregular polygon and how to find the area of an irregular polygon. You will understand how to partition irregular polygons into plane figures and use the formula for each plane figure to find the area.

What's an Irregular Polygon?

Irregular polygons are polygons that do not have equal sides or equal angles. To understand what an irregular polygon is, you must understand what it is not. Let's first consider a square. It has four angles that are 90 degrees and four sides that are all the same length. All of its sides and all of its angles are equal. Therefore, a square is not an irregular polygon. Let's look at some examples of regular and irregular polygons:

Regular and Irregular Polygons
Polygon Chart

Area of an Irregular Polygon

To find the area of an irregular polygon you must first separate the shape into regular polygons, or plane shapes. You then use the regular polygon area formulas to find the area of each of those polygons. The last step is to add all those areas together to get the total area of the irregular polygon.

Let's look at some formulas for finding the area of polygons. Remember that:

b = base

h = height

a = length of a side

w = width

Area of a triangle = 1/2 x b x h

Area of a square = a2

Area of a rectangle = w x h

Area of a parallelogram = b x h

Example 1

Let's start with the following shape:

Irregular Polygon
Irregular Polygon

If we partition, or separate, this shape it will look like this:

Partitioned Irregular Polygon
Partitioned Irregular Polygon

We have to use the formula for rectangles since the irregular polygon has been partitioned into three different rectangles. The first rectangle has measurements of the width being 4 cm and the height is 6 cm. Using the formula, we need to multiply 4 cm by 6 cm. Our product will be 24 cm2. So, the area of rectangle one is 24 cm2. Here's the formula:

Area = w x h = 4 cm x 6 cm = 24 cm2

We square the product because we're multiplying two different dimensions: the height and width of a plane shape. Now we move to the second rectangle which has a width of 5 cm and a height of 4 cm. Using the same formula:

Area = w x h = 5 cm x 4 cm = 20 cm2

The third rectangle has a width of 4 cm and a height of 9 cm. The formula is as follows:

Area = w x h = 4 cm x 9 cm = 36 cm2

The last step is to add the products of all the formulas for all the rectangles. This will give us the area of the entire irregular polygon. Since it was partitioned into three different rectangles, we add all three products.

24 cm2 (rectangle 1) + 20 cm2 (rectangle 2) + 36 cm2 (rectangle 3) = 80 cm2

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