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# Composite Figures – Area and Volume

Nov 26, 2022

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book.

To understand the dynamics of composite figures, one needs first to cover the basics of real two-dimensional geometric figures. Because at the end of the day, composite figures are the sum of basic figures.

## Basic Properties of Two-Dimensional figures:

### Area of Composite Figures

The area of composite figures is the area that any composite shape covers. A composite shape comprises a few polygons that are joined together to form the desired shape. These shapes or figures can be made up of triangles, squares, and quadrilaterals, among other things. To calculate the area of a composite shape, divide it into basic shapes such as squares, triangles, rectangles, hexagons, etc.

A composite shape is made up of basic shapes that have been combined. It is also referred to as a “composite” or “complex” shape.

Now that we have figured out the basic properties of the important polygons, we can move into understanding the area and perimeter of the polygons:

### The volume of Composite Figures

Understanding volume when it comes to finding areas is crucial. You must know the volumes to calculate areas of various sections when limited data is provided. In mathematical terms, volume is the amount of space inside a 3-D object. First, we will understand some basic terms needed to find the volume of composite figures. Then we will get into the formulae.

Solid Figure: Three-dimensional figures of simple geometric shapes are called solid figures. Some examples of solid figures are cubes, prisms, pyramids, and cylinders. The volume of a Solid figure: The volume of a solid figure is the measure of the enclosed space within the figure.

Composite Figure: Figures constructed by connecting different solid figures are composite figures. The volume of a Composite Figure: Sum of the volumes of the given solid figures.

Let us understand the properties of some basic 3D objects like the way we discussed for the 2D objects:

#### How to Find Volume of a Composite Figure?

• Measure the dimensions of the bottom solid figure and find the volume.
• Measure the dimensions of the top solid figure and find the volume.
• Find the volume of the composite figure by adding the volume of the two solid figures.

Some of the important formulae regarding finding the surface areas and volumes of various composite figures:

### How to find the area of a Composite Figure?

Finding the areas of composite figures is not much challenging. You have to memorize the formulae by heart and do the calculations. You can score more if you learn the formulae and practice them regularly. The area of the composite figures is the area of one or more simple polygons and circles combined. We can add the areas of all the basic figures together to calculate the area of the composite figures. Find the area of each shape and add them together to find the area of the composite figure. For example, the area of composite shapes is measured in m2, cm2, in2, or ft2.

Example:

1. Find the area of the composite figure when – 1. There is a rectangle of 4cm and 3cm in height & length, respectively. 2. A triangle with a 5cm base, 10cm height

A: As we have learned in the past, a composite figure is a summation of basic polygons. So to find the area of composite figures, we have to break the figure into small polygons and then apply the formula as required.

Hence the area of the rectangular- 4 x 3 = 12 square cm

Area of the triangle – ½ x 10 x 5 = 25 square cm

Therefore, the total area of the composite figure = 12 + 25 = 37 square cm

1. A composite figure has an area of 100 units square. The shape is composed of a circle and a triangle, and the area of the triangle is 64 units square. What is the area of the circle?

A: Given the area of the composite figure = 100 units square and the area of the triangle = 64 units square

Using the formula for the area of the composite shape, Area of composite shape = area of triangle + area of the circle.

⇒ 100 = 64 + area of circle

⇒ Area of circle = 100 – 64

⇒ Area of the circle = 36 units square.

Therefore the area of the circle is 36 units square.

### 1. What is a composite figure?

Ans. A composite figure is a drawing that represents multiple objects. Composite figures are often found in art, where they can be used to create the illusion of depth.

### 2. What is composite figure formula?

Ans. Composite figure formula is a formula to find the area of a composite figure. The formula is:

Area = (Area of rectangle) + (Area of triangle)

The rectangle is the area between the x-axis and y-axis, while the triangle is the area between the x-axis and line y=k.

### 3. What is a composite figure or shape?

Ans. A composite figure is a shape that is made up of two or more other shapes.It can be difficult to determine which shapes combine to make one composite shape, and this can be a problem for people with dyslexia.

### 4. How do you find the value of composite figures?

Ans. You can find the value of composite figures by adding together the values of their component parts. For example, if you have a composite figure made up of two triangles and one square, you add up the values of each triangle and then add them to the value of the square.

### 5. How do you find the length of a composite figure?

Ans. The length of a composite figure is the sum of all of its component parts. The formula for finding the length of a composite figure is length = ∑(length of each component)

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