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AREA OF COMPOSITE FIGURES

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AREA OF COMPOSITE FIGURES

- A composite figure is made of triangles, quadrilaterals, semicircles, and other 2-D figures.
- A semicircleis half of a circle.
- Examples:

TRIANGLE

RECTANGLE

SEMICIRCLE

TRAPEZOID

To find the area of a composite figure, separate it into figures with areas you know how to find. Then add those areas.

AREA OF COMPOSITE FIGURES

- Let’s find the area of the following composite figure.

6 cm

This figure can be separated into a rectangle and a semicircle. Now we just find the area of each figure.

3 cm

14 cm

AREA OF SEMICIRCLE:

A = r2(this is area of a

2 circle, cut in ½)

A = 3.14 4 4

2

A = 50.24 = 25.12 cm2

2

AREA OF RECTANGLE:

A = lw

A = 14 3

A = 42 cm2

BOTH AREAS ADDED TOGETHER:

42 + 25.12 = 67.12 cm2

AREA OF COMPOSITE FIGURES

- Now you try to find the area of the following composite figure.

This figure can be separated into a triangle and ¾ of a circle. Now we just find the area of each figure.

3 cm

Together:

18 + 21.195 = 39.195 cm2 for the area of the composite figure.

12 cm

AREA OF CIRCLE:

A = r2(this is area of a WHOLE

circle)

A = 3.14 3 3

A = 28.26 cm2 (WHOLE CIRCLE)

Now, we only need area for 3 parts of the circle ; so we need to divide the area by 4 to get ¼ then multiply by 3 to get ¾. 28.26 ÷ 4 = 7.065.

7.065 3 = 21.195 cm2 is ¾ of circle.

AREA OF TRIANGLE:

A = bh

2

A = 12 3

2

A = 36 = 18 cm2

2

AREA OF COMPOSITE FIGURES

- Now you try again to find the area of the following composite figure.

This figure can be separated into a square & a rectangle. Now we just find the area of each figure.

9 cm

6 cm

3 cm

12 cm

AREA OF SQUARE:

A = side side

A = 3 3

A = 9 cm2

AREA OF RECTANGLE:

A = bh

A = 12 3

A = 36 cm2

Together:

9 + 36 = 45 cm2 for the area of the composite figure.

AREA OF SHADED PARTS OF FIGURES

- Sometimes you have to find the area of the shaded region in each figure.
- This figure is a large circle with a small circle inside it.
- To find the area of just the shaded part (the outer circular part),
- we need to find the area of both the larger circle and the smaller
- white filled circle, and then subtract the two areas to get just the
shaded circle’s area.

6 m

8 m

AREA OF SMALL CIRCLE:

A = r2

A = 3.14 3 3

A = 28.26 m2

AREA OF LARGE CIRCLE:

A = r2

A = 3.14 4 4

A = 50.24 m2

Now, we take the 2 areas and subtract:

50.24 – 28.26 = 21.98 m2

AREA OF SHADED PARTS OF FIGURES

- Now you try
- This figure is a large circle inside a square.
- Find the area of only the rectangle part showing around the circle.

6 m

12 m

AREA OF SQUARE:

A = s2

A = 12 12

A = 144 m2

AREA OF CIRCLE:

A = r2

A = 3.14 6 6

A = 113.04 m2

Now, we take the 2 areas and subtract:

144.00 – 113.04 = 30.96 m2