Area of Composite Figures (How-To w/ 19 Step-by-Step Examples!)

In today’s geometry lesson, you’re going to learn all about the area of composite figures.

Jenn (B.S., M.Ed.) of Calcworkshop® teaching area of composite figures

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

You’ll learn how basic polygons (squares, rectangles, etc.) are used to determine the area of many complex figures.

So let’s jump on in!

Did you know that any polygonal region can be divided into nonoverlapping regions?

This means that we can take any complex shape and divide it into known polygons!

Why is this important?

Because the area of the complex shape is equal to the sum of the areas of the divided nonoverlapping regions!

Area Formulas

Together we will learn how to use formulas to find the area of the following basic polygons:

Rectangle

Area = lw , where l = length and w = width

Area of a Rectangle

Square

Area = x^2 , where x is the length of one side of the square

Area of a Square

Triangle

Area = 1/2*b*h , where b = base and h = height

Area of a Triangle

Equilateral Triangle

Area = SQRT(3)/4*x^2 , where x = length of side

Area of Equilateral Triangle

Parallelogram

Area = bh ; where b = length of the base, and h = length of the altitude of the parallelogram

Area of a Parallelogram Formula

Rhombus

Area = (1/2)d1*d2 , where d1 = length of first diagonal, and d2 = length of second diagonal

Rhombus Area Formula

Trapezoid

Area = (1/2)*h*(b1 + b2) , where h = height, b1 = length of base one, and b2 = length of base two

Trapezoid Area Formula

And then, we will use these formulas for finding the area of basic polygons, to find the area of composite figures.

A composite figure, sometimes referred to as complex figures or shapes, as Khan Academy nicely states, is a figure comprised of two or more basic polygons.

Let’s take a look at a basic example to clarify the process. Notice that the given polygon is comprised of both a square and a triangle. Therefore, if we find the area of the square and the area of the triangle separately, then the total area of the polygon is the sum of these two areas.

How To Find The Area Of A Composite Figure

In the video below, you’ll learn how to set up and solve many different types of problems. Including the tricky ones…

…and lastly, you find out how to use ratios and proportions to find area or lengths of geometric figures too.

Video – Lesson & Examples

1 hr

Introduction to Video: Area of Polygons and Complex Figures
00:00:27 – Formulas for Finding Area of a Rectangle, Square, Triangle, Parallelogram, Rhombus, and Trapezoid
Exclusive Content for Member’s Only

00:12:12 – Find the area of the polygon or the side length given the area (Examples #1-6)
00:20:56 – Find the indicated area or length of a polygon (Examples #7-12)
00:30:09 – Finding area of composite figures (Examples #13-15)
00:40:27 – Using ratios and proportions find the area or side length of a polygon (Examples #16-17)
00:49:51 – Using ratios and proportions find the area or length of a diagonal of a rhombus (Examples #18-19)
Practice Problems with Step-by-Step Solutions
Chapter Tests with Video Solutions

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