FINDING THE AREA OF A COMPOSITE FIGURE

Example 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

= 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)

= (1/2)(1.5)(7 + 10)

= (1/2)(1.5)(17)

= 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

= 27.75

So, the area of the given composite figure is 27.75.

Example 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

= (1/2)(3)(2)

= 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

= 11 x 4

= 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

= (1/2)(3)(3)

= 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

= 51.5

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

Example 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

= 10 x 10

= 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

= (1/2)(3.14)(5)²

= 1.57 x 25

= 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

= 139.25

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

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