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Q.

A room is constructed along with the verandah around it surrounding all the four sides of the room. Dimensions of the room are 5.5 m long and 4 m wide. Verandah is of width 2.25 m. Find the area of the verandah constructed?

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a

63 m^{2}

b

65 m^{2}

c

60 m^{2}

d

68 m^{2}

answer is A.

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Detailed Solution

Concept: Firstly, we’ll divide the verandah into smaller rectangles, and then we’ll calculate the dimensions of those rectangles and after that we’ll find the area of those rectangles and then add them to get the area of the verandah.
Consider a room

ABCD

and the surrounding area, its verandah.
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Now,

AB = 5.5 m

,

BC = 4 m

and the width of the verandah is

2.25 m

.
So,

ID = JA = LB = CK = 2.25 m

Area of veranadah = area of EFIJ + area of DIKC + area of LKGH + area of JABL

We know,

JI = JA + AD + DI = 2.25 + 4 + 2.25 = 8.5 m

FI = 2.25 m

JL = IK = AB = 5.5 m

LH = 2.25 m

LK = JI = 8.5 m

Area of rectangle EFIJ = JI ✕FI = 8.5 m \times 2.25 m

Area of rectangle EFIJ = 19.125 m^{2}

We know that,

Area of rectangle LKGH = Area of rectangle EFIJ

Area of rectangle LKGH = 19.125 m^{2}

Area of rectangle DIKC = DI ✕IK = 2.25 m \times 5.5 m

Area of rectangle DIKC = 12.375 m^{2}

We know that,

Area of rectangle JABL = Area of rectangle DIKC

Area of rectangle JABL = 12.375 m^{2}

Now,

Area of the verandah = 19.125 + 19.125 + 12.375 + 12.375

Area of the verandah = 63 m^{2}

Hence, the area of verandah is

63 m^{2}

.

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A room is constructed along with the verandah around it surrounding all the four sides of the room. Dimensions of the room are 5.5 m long and 4 m wide. Verandah is of width 2.25 m. Find the area of the verandah constructed?