# FINDING THE AREA OF A COMPOSITE FIGURE WORKSHEET

## About "Finding the area of a composite figure worksheet"

Finding the area of a composite figure worksheet :

Worksheet on finding the area of a composite figure is much useful to the students who would like to practice problems on composite figures.

## Finding the area of a composite figure worksheet - Problems

1.  Find the area of the figure given below.

2.  Find the area of the figure given below.

3.  Find the area of the figure given below.

## Finding the area of a composite figure worksheet - Solution

Problem 1 :

Find the area of the figure given below.

Solution :

Step 1 :

Separate the figure into smaller, familiar figures: a parallelogram and a trapezoid.

Step 2 :

Find the area the parallelogram.

Base (b)  =  10 cm

Height (h)  =  1.5 cm

Use the formula.

A  =  bh

A  =  10 · 1.5

A  =  15

The area of the parallelogram is 15 square cm .

Step 3 :

Find the area the trapezoid.

Base₁ (b₁)  =  7 cm

Base₂ (b₂)  =  10 cm

Height (h)  =  1.5 cm

Use the formula.

A  =  (1/2)h(b₁+b₂)

A  =  (1/2)(1.5)(7+10)

A  =  (1/2)(1.5)(17)

A  =  12.75

The area of the trapezoid is 12.75 square cm.

Step 4 :

Add the areas to find the total area.

A  =  15 + 12.75

A  =  27.75

Hence, the area of the given composite figure is 27.75

Problem 2 :

Find the area of the figure given below.

Solution :

Step 1 :

Separate the figure into smaller, familiar figures: a two triangles and a rectangle.

Step 2 :

Find the area the first triangle.

Base (b)  =  3 ft

Height (h)  =  2 ft

Use the formula.

A  =  (1/2)bh

A  =  (1/2)(3)(2)

A  =  3

The area of the first triangle is 3 square ft.

Step 3 :

Find the area the rectangle.

Length (l)  =  8 + 3  =  11 ft

Height (h)  =  4 ft

Use the formula.

A  =  l x w

A  =  11 x 4

A  =  44

The area of the rectangle is 44 square ft.

Step 4 :

Find the area the second triangle.

Base (b)  =  3 ft

Height (h)  =  3 ft

Use the formula.

A  =  (1/2)bh

A  =  (1/2)(3)(3)

A  =  4.5

The area of the second triangle is 4.5 square ft.

Step 5 :

Add the areas to find the total area.

A  =  3 + 44 + 4.5

A  =  51.5

Hence, the area of the given composite figure is 51.5 square feet.

Problem 3 :

Find the area of the figure given below.

Solution :

Step 1 :

Separate the figure into smaller, familiar figures: a square and a semicircle.

Step 2 :

Find the area the square.

Length of each side  =  10 m

Use the formula.

A  =  Side x Side

A  =  10 x 10

A  =  100

The area of the rectangle is 100 square meter.

Step 3 :

Find the area the semicircle.

Diameter  =  10 m

Radius (r)  =  Diameter / 2  =  10/2  =  5 m

Use the formula.

A  =  (1/2)πr²

A  =  (1/2)(3.14)(5)²

A  =  1.57 x 25

A  =  39.25

The area of the semi circle is about 39.25 square meter.

Step 4 :

Add the areas to find the total area.

A  =  100 + 39.25

A  =  139.25

Hence, the area of the given composite figure is about 139.25 square meter.

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