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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Bethany Calderwood*

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

Finding the areas of shapes is an important part of geometry. Area is used in math and science as well as in architecture and interior decorating. In this lesson, we'll learn how to find the area of an irregular hexagon.

A hexagon is a shape with six sides. In a regular hexagon, all six sides are equal. An **irregular hexagon** is a six-sided shape whose sides are not equal.

Ellia's grandma is helping her make a quilt. The quilt's background is black, and Ellia is going to sew brightly colored shapes on it. She has drawn some irregularly-shaped hexagons for her quilt. Grandma wants her to find the area of each irregular hexagon so she knows how much fabric they'll need all together.

**Area** refers to the measurement of a 2-dimensional surface: in this case, the size of the quilt or its individual parts. In order to find the area of Ellia's irregular hexagons, we first need to know how to find the area of two other shapes: rectangles and right triangles.

To find the **area of a rectangle**, multiply the length of the rectangle times the width of the rectangle.

*area = length * width*

A right triangle is one half of a rectangle and has one ninety-degree angle. To find the **area of a right triangle**, start by multiplying the base times the height, and then divide the answer by two:

*area* = (*base * height*) / 2

Now that we know how to find the area of rectangles and triangles, we're ready to find the area of Ellia's hexagons.

There's no specific formula for finding the area of a hexagon. Rather, we need to organize the hexagon into rectangles and right triangles and find the area of each shape. Ellia's hexagon can be broken down into two rectangles and two right triangles, as shown by the red lines in the image, and labeled A, B, C, and D.

Shape A is a rectangle. The length is 8 inches and the width is 4 inches.

*area = length * width*

8 * 4 = 32

The area of shape A = 32 in2

Shape B is a rectangle. The length is 4 inches and the width is 2 inches.

*area = length * width*

4 * 2 = 8

The area of shape B = 8 in2

Shape C is a right triangle. The base is 2 inches and the height is 2 inches.

*area* = (*base x height*) / 2

(2 * 2) / 2 = 4 / 2 = 2

The area of shape C = 2 in2

Shape D is also a right triangle. Its measurements are exactly the same as those for Shape C, so we know that the area will be the same. To check, we will do the math:

*area* = (*base * height*) / 2

(2 * 2) / 2 = 4 / 2 = 2

The area of shape D = 2 in2

The areas of A + B + C + D = the area of the hexagon

32 + 8 + 2 + 2 = 44

The area of Ellia's hexagon is 44 in2.

An **irregular hexagon** has six unequal sides. To find the total area of an irregular hexagon, organize it into rectangles and right triangles and find the area of each geometric shape using these formulas:

**area of a rectangle:**

*area*=*length * width*

**area of a right triangle:**

*area*= (*base * height*) / 2

Then, add the areas of the different geometric components together.

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41 in chapter 2 of the course:

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Math for Kids23 chapters | 325 lessons

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