**Finding the area of a composite figure :**

A composite figure is made up of simple geometric shapes.

To find the area of a composite figure or other irregular-shaped figure, divide it into simple, non overlapping figures.

Find the area of each simpler figure, and then add the areas together to find the total area of the composite figure.

We can use the chart below to review some common area formulas.

**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

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

**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

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.

**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

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".

Apart from the stuff given above, if you want to know more about "Finding the area of a composite figure", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**