**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.

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.

**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.

After having gone through the stuff given above, we hope that the students would have understood "Finding the area of a composite figure worksheet".

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