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# Area of Composite Figures Worksheet, Examples, and Formula

Get the free Area of Composite Figures Worksheet and other resources for teaching & understanding Area of Composite Figures

Finding Area of Composite Figures in 3 EASY steps (Area of Composite Shapes)

### Key Points

• Composite figures are made up of two or more shapes combined together to form one figure.
• To find the area of composite figures, one must break the figure down into simpler shapes and add up their areas.
• Understanding the area of composite figures is essential in many fields, including architecture, engineering, and design.

## The Complete Guide for finding Area of Composite Shapes

Area of composite figures is a topic that is often studied in mathematics because it is a fundamental concept. Composite figures are made up of two or more shapes combined together to form one figure. These shapes may be of different sizes and types, and may be arranged in various ways. Knowing how to calculate the area of composite figures is essential in many fields, including architecture, engineering, and design.

To find the area of composite figures, one must first break the figure down into simpler shapes and then add up the areas of those shapes. The simpler shapes may include rectangles, triangles, circles, or trapezoids. There are several formulas that can be used to find the area of each of these shapes, and once the areas are calculated, they can be added together to find the total area of the composite figure.

By understanding the concepts and formulas for finding the area of composite figures, individuals can apply this knowledge to real-life scenarios. For example, architects may need to calculate the area of a building’s floor plan, which may include composite figures such as L-shaped rooms or hallways. Similarly, engineers may need to calculate the area of a cross-section of a bridge or tunnel, which may also be a composite figure. By having a solid understanding of the area of composite figures, one can approach these scenarios with confidence.

A Composite Figure is a 2-D figure that has an unusual shape. Composite Figures can be made up of many different shapes. In order to find how to find Area of Composite Figures you have to break the figure up into individual shapes. Usually you will break the Composite Figure up into squares, rectangles, and triangles. Once the Composite Figure is broken up into individual shapes you can find the area of each individual shape and then add them together. The sum of all the areas of the individual shapes will be the area of the Composite Figure.

Common Core Standard: 6.G.1
Related Topics: Area of a Triangle, Area of a Parallelogram, Area of a Trapezoid

## What are Composite Figures?

Composite figures are geometric shapes that are made up of two or more basic shapes. These shapes can be combined in a variety of ways to create a new, more complex shape. Composite figures can be found in many real-world situations, such as in architecture, art, and engineering.

Composite figures can be made up of any combination of basic shapes, including triangles, rectangles, circles, and more. Some common examples of composite figures include L-shaped figures, figures with cutouts, and figures with curved edges.

When calculating the area of a composite figure, it is important to break the figure down into its basic shapes. This makes it easier to calculate the area of each individual shape and then add them together to find the total area of the composite figure.

Composite figures can also be used to calculate the perimeter of a shape. The perimeter is the distance around the outside of a shape. To find the perimeter of a composite figure, simply add up the lengths of all the sides of the individual shapes that make up the composite figure.

Overall, composite figures are important in many areas of math and science. They are used to calculate the area and perimeter of complex shapes, and they can be found in many real-world situations. By breaking down composite figures into their basic shapes, it is possible to calculate their properties and use them in a variety of applications.

## How to Find Area of Composite Figures

Calculating the area of composite figures can seem daunting, but it can be broken down into simple steps. The first step is to decompose the composite figure into basic shapes, such as triangles, rectangles, and circles.

Once you have identified the basic shapes, use their respective area formulas to calculate their individual areas. For example, the area of a triangle is calculated by multiplying the base by the height and dividing the result by 2. The area of a rectangle is calculated by multiplying the length by the width. The area of a circle is calculated by multiplying pi by the radius squared.

After you have calculated the areas of the basic shapes, add them together to find the total area of the composite figure. Remember to use the same units of measurement throughout the calculation.

Here is an example:

Suppose you have a composite figure made up of a rectangle and a triangle. The rectangle has a length of 8 units and a width of 4 units. The triangle has a base of 4 units and a height of 6 units.

To find the area of the rectangle, multiply 8 by 4 to get 32 square units. To find the area of the triangle, multiply 4 by 6 and divide by 2 to get 12 square units.

Finally, add the areas of the rectangle and triangle to get the total area of the composite figure, which is 44 square units.

In summary, to find the area of a composite figure, decompose it into basic shapes, calculate the area of each shape using its respective formula, and add the areas together.

## 4 Easy Steps for Solving Area of Composite Figures Examples

Composite figures are shapes that are made up of two or more simpler shapes. In order to calculate the area of a composite figure, the area of each simpler shape is calculated and then added together. Here are some examples of composite figures.

1. Break the Area of Composite Figures into smaller shapes such as, rectangles, triangles, and squares.
2. Use the area formula for rectangles, triangles, and squares to find the area of each smaller shape.
3. Add the area of the smaller shapes together to get the area of the entire Composite Figure.
4. Make sure you use the correct unit measure for the area.

### Rectangles and Squares

Rectangles and squares are examples of composite figures. The area of a rectangle is calculated by multiplying its length by its width. The area of a square is calculated by squaring its side length. If a composite figure is made up of rectangles and squares, the area of each individual shape is calculated and then added together to find the total area of the composite figure.

### Triangles and Trapezoids

Triangles and trapezoids are other examples of composite figures. The area of a triangle is calculated by multiplying its base by its height and then dividing by 2. The area of a trapezoid is calculated by adding the lengths of its parallel sides, multiplying the sum by its height, and then dividing by 2. If a composite figure is made up of triangles and trapezoids, the area of each individual shape is calculated and then added together to find the total area of the composite figure.

### Circles and Semicircles

Circles and semicircles are also examples of composite figures. The area of a circle is calculated by multiplying the square of its radius by pi. The area of a semicircle is half the area of a circle with the same radius. If a composite figure is made up of circles and semicircles, the area of each individual shape is calculated and then added together to find the total area of the composite figure.

In summary, composite figures can be made up of rectangles, squares, triangles, trapezoids, circles, and semicircles. To find the area of a composite figure, the area of each individual shape is calculated and then added together.

## 5 Quick Area of Composite Figures Practice Problems

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Composite Figures Quiz

Click Start to begin the practice quiz!

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Find the area of the composite figure.

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Find the area of the composite figure.

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Find the area of the composite figure.

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Find the area of the composite figure.

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Find the area of the composite figure.

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## Finding Area of Composite Figures Formula

When calculating the area of composite figures, it is essential to break down the shape into smaller, more manageable shapes. This allows for the easier calculation of the area of each smaller shape, which can then be added together to find the total area of the composite figure.

The formula for finding the area of a composite figure involves breaking the figure down into simpler shapes such as squares, rectangles, triangles, and trapezoids. Once the figure is broken down, the area of each shape can be calculated using the appropriate formula.

For example, to find the area of a composite figure made up of a rectangle and a triangle, the formula would be:

`Area of Composite Figure = Area of Rectangle + Area of Triangle`

The formula for finding the area of a rectangle is:

`Area of Rectangle = Length x Width`

The formula for finding the area of a triangle is:

`Area of Triangle = 1/2 x Base x Height`

Once the areas of the rectangle and triangle are calculated, they can be added together to find the total area of the composite figure.

Another example of a composite figure is one made up of a rectangle and a trapezoid. The formula for finding the area of this composite figure would be:

`Area of Composite Figure = Area of Rectangle + Area of Trapezoid`

The formula for finding the area of a trapezoid is:

`Area of Trapezoid = 1/2 x Height x (Base 1 + Base 2)`

By breaking down the composite figure into simpler shapes, the area of each shape can be calculated using the appropriate formula, and the areas can be added together to find the total area of the composite figure.

It is important to note that when breaking down a composite figure into simpler shapes, it is essential to ensure that there is no overlap between the shapes. Overlapping shapes can lead to inaccurate calculations and incorrect results.

## Real Life Composite Figures

Composite figures are everywhere in the real world. Architects, engineers, and designers use composite figures to design buildings, bridges, and other structures. Here are some examples of composite figures in real life:

• Floor Plans: Floor plans of buildings often contain composite figures. For example, a room may have a rectangular shape with a smaller rectangular cut-out for a closet or bathroom. To find the area of the room, one would need to calculate the area of the two rectangles and subtract the area of the cut-out.
• Landscaping: Landscapers often use composite figures to design gardens and outdoor spaces. For example, a garden may have a rectangular lawn with a circular flower bed in the center. To calculate the area of the lawn and the flower bed, one would need to calculate the area of the rectangle and the circle separately and then add them together.
• Packaging: Packaging designers often use composite figures to create packaging that fits the product perfectly. For example, a box for a toy may have a rectangular base with a triangular top. To calculate the area of the box, one would need to calculate the area of the rectangle and the triangle separately and then add them together.
• Art and Design: Artists and designers often use composite figures in their work. For example, a painting may have a rectangular canvas with a circular object in the center. To calculate the area of the painting, one would need to calculate the area of the rectangle and the circle separately and then add them together.

Overall, composite figures are an important concept in many fields and are used to solve real-world problems. By breaking down complex shapes into simpler shapes, it becomes easier to calculate their areas and work with them effectively.

## FAQ about how to find Area of Composite Figures

### What is a composite figure?

A composite figure is a two-dimensional shape that is made up of two or more simpler shapes, such as rectangles, triangles, circles, or other polygons. These shapes are combined to create a new shape with a unique area.

### How do I find the area of a composite shape?

To find the area of a composite shape, you need to break it down into simpler shapes that you know how to find the area of. You can then add up the areas of these simpler shapes to get the total area of the composite shape.

### What is the formula to find the area of composite figures?

There is no single formula to find the area of composite figures. Instead, you need to use the formulas for the individual shapes that make up the composite figure. Once you have found the area of each individual shape, you can add them together to find the total area of the composite figure.

### Can you give an example of a composite figure in math?

An example of a composite figure in math is a figure that is made up of a rectangle and a triangle. To find the area of this figure, you would first find the area of the rectangle and then find the area of the triangle. You would then add these two areas together to find the total area of the composite figure.

### How do you solve the area of composite polygons?

To solve the area of composite polygons, you need to break the polygon down into simpler shapes, such as rectangles, triangles, or trapezoids. You can then find the area of each of these shapes and add them together to find the total area of the composite polygon.

### What is an example of a composite figure in math?

Another example of a composite figure in math is a figure that is made up of a rectangle and a semicircle. To find the area of this figure, you would first find the area of the rectangle and then find the area of the semicircle. You would then add these two areas together to find the total area of the composite figure.

## Area of Composite Figures Worksheet Video Explanation

Watch our free video on how to find Area Composite Figures. This video shows how to solve problems that are on our free Area of Composite Shapes worksheet that you can get by submitting your email above.

Watch the free Area of Composite Figures video on YouTube here: Area of Composite Figures Video

Video Transcript:

If you look we have one side that is 30 inches long we have another side that’s 12 inches long. This side right here is 5 inches and this bottom line is 10 inches long. What I’m going to do is I’m going to draw dotted lines to break the figure into two separate rectangles. I’m going to draw a dotted line right here across the middle and I’m going to label this rectangle one. And I’m going to label this one rectangle two. Now we have two separate rectangles in order to find the area of rectangle one. Rectangle one this is a rectangle so the area is length times width. That means we’re going to multiply 30 times 12 and get 360 inches. The area of rectangle 2 is also length times width and the length of this one is 10 inches and the width is 5. The area of rectangle 2 is 5 times 10, which would be 50 inches. In order to find the area of the entire composite figure you have to add the area of this rectangle plus the area of this rectangle. That means we’re going to take 360 because that’s rectangle 1 and add it to the area of rectangle 2 which is 50.  360 plus 50 is 410 inches squared. Our final solution will be 410 inches squared for this composite figure.

Let’s do a couple practice problems on our composite shapes worksheet. Number one on our area of composite figures worksheets gives us side lengths of 8 inches 2 inches 7 inches and 10 inches. It says to find the area of the composite figure. In the case of this problem the only shape that we need in order to find the area of this composite figure is a rectangle. We know the area of a rectangle is equal to length times width. When I find the area of this composite figure, I’m going to break it into two separate rectangles. I could draw a dotted line here and I could use this for a rectangle and this for the second rectangle or I could draw a dotted line here and use this for one rectangle and this for the other rectangle. Whichever way you do it, it does not matter as long as you use the correct side lengths. In order to find the area of rectangle one, I’m going to say area of rectangle 1. This is equal to length times width in the case of this rectangle we have a length of 8 inches. This is going to be our first length. 8 inches times the other side length which is 2 inches. 8 inches times 2 inches so the area of rectangle 1 is 16 inches and I’m going to say this is 16 inches squared. We know this is 16 inches squared the area of rectangle 2 is again length times width because it’s a rectangle this time the length of this rectangle is not 10 inches 10 inches goes from this side all the way to this side. It’s this whole distance right here. We’ve already used this distance from here to here and we’ve already used it in our first rectangle for two inches. We know this is two inches. We’ve already used this. We’ve already accounted for it that means from that dotted line all the way to this side. this has to be eight inches because we’ve already used two inches. this is two inches from here to here, this has to be eight inches from here to here, because the whole thing has to be 10 inches. Our length for our second rectangle is going to be 8 inches because we’ve already used 2 out of the 10 inches then the width is going to be 7 inches because this side we did not change. 8 times 7 is 56 and then in order to get the area of the entire figure you have to add 56 inches squared. The area of the second rectangle plus the area of this first rectangle. We’re going to say 16 inches squared plus 56 inches squared and we’re going to get 72 inches squared and we know the area of this composite figure worksheet is 72 inches squared.

The last problem we’re going to do on our composite figures area worksheet is number four. Our composite figure this time is made up of two separate shapes. We have a rectangle here this is a rectangle and we also have a triangle which is here. We’re going to find the area of the rectangle first and we’re going to find the area of the triangle second and then we’re going to add them together. We know area of a rectangle is length times width and we also know that the area of a triangle is base times the height divided by two. The first thing we’re going to do is find the area of this rectangle. Shape one is length times width. The length in this case is 24 inches and the width is 10 inches so we’re going to do 24 times 10 and we’re going to get 240 inches squared. We know shape 1 is 240 inches squared shape 2 is a triangle. We know that the area is base times the height divided by 2. The base in this case is the distance all the way across from one side of the triangle to the other so we know this distance is the same as this distance because it’s a rectangle. This whole side on the bottom is 24 inches that means the opposite side is also 24 inches. We know the base is 24 inches and they say the height of the triangle is 9 inches. We’re going to do 24 times 9 and get 216 inches and then to find the area of the entire composite figure. We have to add the triangle plus the rectangle. We’re going to add the rectangle which is 240 inches squared plus the triangle which is 216 inches squared the final area of the entire area of composite figures worksheet grade 6 is 456 inches squared. You can try all of these practice problems by downloading our composite figures worksheet with answers above.

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