Chapter 11 . Mensuration

Exercise 11.1

1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

(a)                                  (b)
Solution:  For square field : Here , a=60 m 

The perimeter of the square field =4a

 =4×60 m=240 m

For rectangular field : Here , l=80 m , b= ?

The perimeter of the rectangular field =2l+b

 =280+bm 

A/Q , 280+b=240

⇒80+b=2402

⇒80+b=120

⇒b=120-80

⇒b=40 m 

(a)  The area of the square field =a2

=60×60=3600 m²

(b) The area of the rectangular field =l×b

=80×40=3200 m² 

The square field has a larger area , i.e.,  figure (a)

2. Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per cm2 .
Solution: For square plot :  Here , l=25 m

Area of the square plot =l²=25² m²=625 m²

For rectangular plot : Here , l=20 m and  b=15 m 

Area of the rectangular plot =l×b

=20×15 m²=300 m² 

Area of the garden around the house =625-300=325 m²

The total cost of developing a garden around the house

=Rs55m2×325 m2

=Rs 55×325

=Rs 17875