Answer :

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 cm^{2} …(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 cm^{2} …(ii)

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

A = 25.2 – 8.75

⇒ A = 25.20 – 8.75

⇒ A = 16.45 cm^{2}

**Hence, area of the courtyard without the mattress is 16.45 cm ^{2}.**

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