Area of composite figures
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AREA OF COMPOSITE FIGURES. COMPOSITE FIGURES. A composite figur e is made of triangles, quadrilaterals, semicircles, and other 2-D figures. A semicircle is half of a circle. Examples:. TRIANGLE. RECTANGLE. SEMICIRCLE. TRAPEZOID.

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AREA OF COMPOSITE FIGURES

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Area of composite figures

AREA OF COMPOSITE FIGURES


Composite figures

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

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

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

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 composite figures

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 composite figures

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


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