Q2 of 38 Page 5

The Length and breadth of the rectangular courtyard of the house of Anima are 6m. and 4.2m respectively. We put a mattress of in the middle of the courtyard.Let’s find the area of the courtyard without the mattress and note it down.

We have


Let ABCD be the rectangular courtyard.


AB = CD = 6 m


BC = AD = 4.2 m


Let the mattress be EFGH.


EF = GH = 3.5 m


FG = HE = 2.5 m


We need to find the area of the courtyard without the mattress, that is, the area of the space between ABCD and EFGH.


Let area of the space between ABCD and EFGH denoted by A.


Then, it is given as


A = Area of ABCD (full courtyard) – Area of EFGH (full mattress) …(A)


[Since, if we remove the area of mattress from the area of courtyard, we are left with the area of the courtyard without the mattress]


Let us find the area of ABCD.


Since, ABCD is a rectangle, then


Area of rectangle = length × breadth


⇒ Area of ABCD = AB × BC


given that, AB = 6 cm and BC = 4.2 cm


⇒ Area of ABCD = 6 × 4.2


⇒ Area of ABCD = 25.2 cm2 …(i)


And let us find the area of EFGH.


Since, EFGH is a rectangle, then


Area of rectangle = length × breadth


⇒ Area of EFGH = EF × FG


given that, EF = 3.5 cm and FG = 2.5 cm


⇒ Area of EFGH = 3.5 × 2.


⇒ Area of EFGH = 8.75 cm2 …(ii)


Putting (i) & (ii) in equation (A), we get


A = 25.2 – 8.75


⇒ A = 25.20 – 8.75


⇒ A = 16.45 cm2


Hence, area of the courtyard without the mattress is 16.45 cm2.


More from this chapter

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1

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There is a path of 3m width all around outside the square shaped park of Ajanta Housing Complex. The perimeter of the park including the path is 484 m. Let’s calculate the area of the path.

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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.