Q6 of 38 Page 5

My brother Dipu draws a picture on the entire rectangular sheet of paper whose length is 15 cm and breadth is 8 cm.

A. Let’s calculate the change of area of the paper if the length is twice and the breadth is same.


B. Let’s calculate the change of area of the paper if the breadth is twice and the length is same.


C. Let’s find how many times the area of the paper will be to the area calculated in case (a), if the length and breadth be twice.


D. Let’s calculate the change of area of the paper if length and breadth be half.


We have a rectangular sheet of

Length = 15 cm


Breadth = 8 cm



(A). According to the question,


Original dimensions of the paper are:


Length = 15 cm


Breadth = 8 cm


New dimensions of the paper are:


Length’ = 2 × Length


⇒ Length’ = 2 × 15


⇒ Length’ = 30 cm


Breadth’ = Breadth


⇒ Breadth’ = 8 cm


Let us find the original area.


Since, area of rectangle = Length × Breadth


Then,


Original area = 15 × 8


⇒ Original area = 120 cm2 …(ii)


Now, let us find the new area.


New area is given by,


New area = Length’ × Breadth’


⇒ New area = 30 × 8


⇒ New area = 240 cm2 …(iii)


Change in area is given by,





Hence, the area is doubled.


(B). According to the question,


Original dimensions of the paper are:


Length = 15 cm


Breadth = 8 cm


New dimensions of the paper are:


Length’ = Length


⇒ Length’ = 15 cm


Breadth’ = 2 × Breadth


⇒ Breadth’ = 2 × 8


⇒ Breadth’ = 16 cm


Let us find the original area.


Since, area of rectangle = Length × Breadth


Then,


Original area = 15 × 8


⇒ Original area = 120 cm2 …(ii)


Now, let us find the new area.


New area is given by,


New area = Length’ × Breadth’


⇒ New area = 15 × 16


⇒ New area = 240 …(iii)


Change in area is given by,





Hence, the area is doubled.


(C). According to the question,


Original dimensions of the paper are:


Length = 15 cm


Breadth = 8 cm


New dimensions of the paper are:


Length’ = 2 × Length


⇒ Length’ = 2 × 15


⇒ Length’ = 30 cm


Breadth’ = 2 × Breadth


⇒ Breadth’ = 2 × 8


⇒ Breadth’ = 16 cm


We need to find the number of times the area of the paper calculated with the new dimensions will be to the area calculated in case (A).


Area of paper in case (A) = 240 cm2 …(i)


Let us find the new area.


Since, area of rectangle = Length × Breadth


New area is given by,


New area = Length’ × Breadth’


⇒ New area = 30 × 16


⇒ New area = 480 cm2 …(ii)


New Area = number of times × Area in case (A)


⇒ 480 = number of times × 240



⇒ Number of times = 2


Hence, the new area calculated will be twice the area calculated in case (A).


(D). According to the question,


Original dimensions of the paper are:


Length = 15 cm


Breadth = 8 cm


New dimensions of the paper are:






⇒ Breadth’ = 4 cm


Let us find the original area.


Since, area of rectangle = Length × Breadth


Then,


Original area = 15 × 8


⇒ Original area = 120 cm2 …(ii)


Now, let us find the new area.


New area is given by,


New area = Length’ × Breadth’



⇒ New area = 30 cm2 …(iii)


Change in area is given by,





Thus, new area is � of the original area.


More from this chapter

All 38 →
4

The length and breadth of Mihir’s rectangular garden is 50m. and 30m. respectively. There is a road in the middle of the garden of width 4m. parallel to the length of the garden. This road divides the garden into two rectangular region of equal area. Let’s draw a picture and find out the area of the road and note it down.

A. If the road of width 4 m passing through the middle of the garden is parallel to the breadth and this road divides the garden into two equal parts, then let’s draw a picture and find the area of the road and note it down.


B. If there are two roads of width 4m parallel to the length and breadth of Mihir’s garden passing through the middle and divides the garden into four equal parts, then let’s draw a picture to find the area of the road and note it down.


 5

There is a rectangular field beside our house owned by Papia’s family. The length and breadth of this land is 48 m and 26 m respectively. Papia’s family has built their house on that land leaving a gap of 4-meter width on all sides. Let’s calculate the area of the region in which they have built their house.

 7

I cut three square shaped paper and notice the changes in areas

If - a. Length becomes double.


b. Length becomes half.


 8

The length, breadth and height of the club-house of our village is 7.2 m., 5.5 m. and 4.2 m respectively. There is a door in the room of length 3 m. and breadth 1.8 m. and two windows each of length 2.25 m. and breadth 1.8 m

A. Let’s measure the area of the floor of the club-house and calculate the total expenditure of cementing the floor at the rate of Rs. 62/m2.


B. Let’s measure the area of the inner wall excluding the door and window.


C. Let’s measure the area of the ceiling of the room.


D. Let’s calculate the total expenditure of whitewashing the inner wall and ceiling except the door and windows at the rate of Rs 12/m2.