COMBINED FIGURES

About "Combined figures"

Combined figures :

Here we are going to see how to find the area and perimeter of combined geometric shapes. In our day to day life we see many combined shapes of triangle, rectangle,square and semi circle. To find the area and perimeter of such figures we need to calculate the area separately and then we can add them.

Example 1:

Find the perimeter and area of the following figures:

Solution :

In the above figure we have four semi circles and one square. To find the perimeter of the above figure we have to add the sum of four semicircles and a square.

Diameter of each semicircle is 7 cm from this we can find the radius of semi circle.

Radius = 7/2  =  3.5 cm   

Length of each side of square = 7 cm

The perimeter of the given figure = 4 (perimeter of semicircles) + Perimeter of square

Perimeter of semi circle AEB = Π r

  = (22/7) x 3.5

   =  22 x 0.5

   =  11    

Perimeter of 4 semi circles = 4 (11)

  =  44 cm

Perimeter of square = 4a

here a = 7 cm                      

  =  4 (7)

  =  28 cm

The perimeter of the given figure = 44 cm + 28 cm

                                       = 72 cm

Area of 1 semi circle = Π r²/2

  =  (1/2) x (22/7) x (7/2)²

  =  (1/2) x (22/7) x (7/2) x (7/2)

 =  (1/2) x 11 x (7/2)

 =  77/4

  = 19.25 cm²

Area of 4 semi circles = 4 (19.25)

  =  77

Area of square = a²

  =  (7)²

  =  7 x 7

  =  49 cm²

Area of given figure = Area of 4 semi circles + Area of square

 = 77 + 49 

 = 126 cm²  

Example 2:

Find the area of shaded portion.

Solution:

Area of shaded portion = Area of rectangle - Area of 4 quadrants of circle

Area of rectangle = L x W

Length of rectangle = 15 cm

Width of rectangle = 8 cm

 =  15 x 8

 =  120 cm²

Area of quadrant = Π r²/4

= [(22/7) x 3²]/4

= (22 x 3 x 3)/(7 x 4)   

= 198/28

Area of 4 quadrant = 4 x 198/28

 =  198/7

  =  28.28 cm²

Area of shaded portion  =  120 - 28.28

 =  91.715 cm²

Related Topics

• Perimeter of sector
  
• practice questions with solution
• Length of arc
• Practice questions on length of arc
  
• Perimeter of square 
• Perimeter of parallelogram
• Perimeter of rectangle
• Perimeter of triangle
• Area of a circle
• Area of Semicircle
• Area of Quadrant
  
• Area of sector
  
• Area of triangle
• Area of equilateral triangle
• Area of scalene triangle
  
• Area of square
  
• Area of rectangle
• Area of parallelogram
• Area of rhombus
• Area of trapezium
• Area of quadrilateral
  
• Area around circle
• Area of pathways

After having gone through the stuff given above, we hope that the students would have understood "Combined figures"

Apart from the stuff given above, if you want to know more about "Combined figures", 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.

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6