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Area of Composite Figures in Two Dimension


A composite figure is a figure composed of several geometric figures. It is important that you learn to recognize the different figures that make up composite figures in order to deal with them effectively. You will often have to find the area of a composite figure, and this will be easier if you can divide the figure into geometric figures that you already know how to find the area of.

Composite figures of squares, triangles and circles

Composite figures of squares, triangles and circles

In the figure above you have several known figures, and it shows a process for how to divide the large figures into smaller figures. There’s never just one way to partition a figure, so if you find another way, it’s just as correct!

Now that you understand how to split up a composite figure, let’s look at five examples where we’ll find the area of a composite figure.

Example 1

Find the area of the house: Assume the square has sides of 5cm and the triangle has a height of 4.33cm

Example of composite figure of triangle and square

To find the total area, you have to find the area of the square and the triangle separately first, and then add them together: A = 5cm 5cm + 5cm 4.33cm 2 25cm2 + 10.83cm2 35.83cm2

Example 2

Find the area of the composite figure:

Example of composite figure of square and trapezoid 1

Just as in the previous example, you have to find the area of the square and the trapezoid separately. Then you add the two areas together to find the area of the entire figure:

A = 4cm 4cm = + (5cm + 3cm) 2cm 2 = 16cm2 + 8cm2 = 24cm2

A = 4cm 4cm + (5cm + 3cm) 2cm 2 = 16cm2 + 8cm2 = 24cm2

Example 3

Find the area of the composite figure:

Example of composite figure of square and trapezoid 2

You divide the figure into a square and a trapezoid, and find those areas separately. Then you sum up the two areas to find the area of the entire figure:

A = 5cm 5cm = + (6cm + 3cm) 4cm 2 = 25cm2 + 18cm2 = 43cm2

A = 5cm 5cm + (6cm + 3cm) 4cm 2 = 25cm2 + 18cm2 = 43cm2

Example 4

Find the area of this figure:

Composite figure of half circle, square and triangle

You need to begin by finding the area of each of the known figures: The rectangle (red), the triangle (gray) and the semicircle (blue). Then you can add the areas together: Asemicircle = π 42 cm2 2 25.12cm2 Arectangle = 5cm 4cm = 20cm2 Atriangle = 4cm 5cm 2 = 10cm2

Awhole = Asemicircle + Arectangle = + Atriangle 25.12cm2 + 20cm2 = + 10cm2 55.12cm2

Awhole = Asemicircle + Arectangle + Atriangle 25.12cm2 + 20cm2 + 10cm2 55.12cm2

Example 5

Find the area of the composite figure

Example of complex Composite figure

You begin by finding the area of the different figures separately, and then you add the areas together:

Aentire figure = Atriangle + Atrapezoid = + Aparallelogram

Acomposite figure = Atriangle + Atrapezoid + Aparallelogram

Finding all the areas will look like this:
Atriangle = base height 2 = 2cm 1cm 2 = 1cm2 Atrapezoid = (a + b) height 2 = (5cm + 2cm) 2cm 2 = 7cm2 Aparallelogram = length height = 5cm 2cm = 10cm2 Aentire figure = Atriangle + Atrapezoid = + Aparallelogram = 10cm2 + 7cm2 = + 1cm2 = 18cm2

Atriangle = baseline height 2 = 2cm 1cm 2 = 1cm2 Atrapezoid = (length 1 + length 2) height 2 = (5cm + 2cm) 2cm 2 = 7cm2 Aparallelogram = length height = 5cm 2cm = 10cm2 Afigure = Atriangle + Atrapezoid + Aparallelogram = 10cm2 + 7cm2 + 1cm2 = 18cm2

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