**Area of composite figures 7th grade :**

Here we are going learn how to find the area of compound figures.

**What is compound figures ?**

Combination of two or more shapes in a single picture is known as compound figures.

Let us see some example problems based on the above concept.

**Example 1 :**

Find the area of the following figure

**Solution :**

By drawing a line GD parallel to AB, we can split the given picture as two parts.

(i) GDEF is a square of side length 3 cm

(ii) ABCG is a rectangle of length 10 cm and width 4 cm

Area of square = a²

Area of rectangle = length x breadth

Area of square (GDEF) = 3² = 9 cm²

Area of rectangle = 10 x 4 = 40 cm²

Area of the given figure = 40 + 9 = 49 cm²

**Example 2 :**

Find the area of the following figure

**Solution :**

By drawing a line BD parallel to AE, we can split the given picture as two parts.

(i) BCD is a triangle

(ii) ABED is a rectangle

Area of triangle = (1/2) x b x h

Area of rectangle = length x breadth

length of AC = 17

AB + BC = 17 ==> 10 + BC = 17 ==> BC = 7 cm

Area of triangle = (1/2) x 7 x 5 = 35/2 ==> 17.5 cm²

Area of rectangle = 10 x 5 = 50 cm²

Area of given shape = 17.5 + 50 ==> 67.5 cm²

**Example 3 :**

John bought a square plot of side 60 m. Adjacent to this David bought a rectangular plot of dimension 70 m x 50 m. Both paid the same amount. Who is benefited ?

**Solution :**

To find who is benefited, we have to find the area of above shapes separately.

(i) ABFG is a square of side length 60 m

(ii) BCDE is a rectangle of length 70 m and width 50 m.

Area of square = a²

Area of rectangle = length x breadth

Area of ABFG = 60² = 60 x 60 = 3600 m²

Area of rectangle = 70 x 50 = 3500 m²

From the above calculation, we come to know that John is having more area than David. So John is more benefited.

**Example 4 :**

Find the area of the following figure

**Solution :**

(i) ABCD is a square of side length 15 cm

(ii) Area of rectangle FEGH

Length of DC = 15

DF + FE + EC = 15 ==> 3 + FE + 5 = 15

FE = 15 - 8 ==> FE = 7 cm

Area of square (ABCD) = a² ==> 15² ==> 225 cm²

Area of rectangle (FEGH) = length x width

= 20 x 7 = 140 cm²

Area of the given figure = 225 + 140 = 365 cm²

**Example 5 :**

Daniel bought a square plot of side 50 m. Adjacent to this Richard bought a rectangular plot of length 60 m and breadth 40 m for the same price. Find out who is benefited and how many sq. m. are more for him?

**Solution :**

Area of square plot = a²

Side length of square = 50 m

Area of land owned by Daniel = 50²

= 50 x 50 = 2500 m²

Area of land owned by Richard = length x width

= 60 x 40 = 2400 m²

Since Daniel is having more area than Richard, we can decide that Daniel is benefited.

Daniel is having 100 m² more area than Richard.

After having gone through the stuff given above, we hope that the students would have understood "Area of composite figures 7th grade".

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