AREA OF COMPOSITE FIGURES 7TH GRADE

A composite figure is made up of several simple geometric figures such as triangles, rectangles, squares, circles, and semicircles.

To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together.

Be sure than none of the simpler figures have overlapping areas.

Example 1 :

Find the area of the figure shown below. 

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  breadth

Area of square (GDEF)  =  32  =  9 cm2

Area of rectangle  =  10  4  =  40 cm2

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

Example 2 :

Find the area of the figure shown below. 

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)  b  h

Area of rectangle  =  length  breadth

length of AC  =  17

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

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

Area of rectangle  =  10  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 figure shown below. 

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  50

= 2500 m2

Area of land owned by Richard = length  width

  =  60  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.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Quadratic Equation Word Problems Worksheet with Answers

    Oct 07, 22 12:25 PM

    Quadratic Equation Word Problems Worksheet with Answers

    Read More

  2. Problems on Quadratic Equations

    Oct 07, 22 12:20 PM

    Problems on Quadratic Equations

    Read More

  3. SAT Math Practice Worksheets

    Oct 07, 22 09:38 AM

    SAT Math Practice Worksheets - Topic wise worksheet with step by step explanation for each question

    Read More