Let’s take a rectangle

51.jpg

And add a semicircle on top of side CD & AB

52.jpg

 

What will be the area of total figure?

54.jpg

 

Area of total figure = Area of rectangle + Area of top semicircle + Area of bottom semicircle.

 

So, area gets added

 

Let’s take some values & actually solve it

 

What will be the area of the figure given below?

55.jpg

 

Here,

Area of total Figure =  Area of rectangle  + Area of top semicircle + Area of bottom semicircle

 

Here, Both semicircle will have the same diameter,

So, their area will be the same

 

∴ Area of total figure = Area of rectangle + 2 × Area of semicircle

Let’s find them out separately

 

Area of rectangle

56.jpg

 

Length = l = AB

      = 20 cm

 

Breadth = b = BC

      = 5 cm

 

Area of rectangle ABCD = l × b

     = AB × BC

     = 20 × 5

     = 100 cm 2

 

Area of semi-circle

57.jpg

Diameter = 20 cm

 

   Radius = r = Diameter/2

        = 20/2

= 10 cm

 

Now,

  Area of semi-circle = (Area of circle)/2

  = πr2/2

  = (3.14  (10)^2)/2

  = (314 × 100)/(100 × 2)

  = 314/2

  = 157 cm 2

Now,

  Area of figure = Area of rectangle ABCD + 2 Area of semi-circle

 = 100 + 2 × (157)

 = 100 + 314

 = 514 cm 2

∴ Area of given figure is 514 cm 2

 

 

 

  1. Chapter 11 Class 7 Perimeter and Area
  2. Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.