MathematicsA 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?

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?


  1. A
    63m2
  2. B
    65m2
  3. C
    60m2
  4. D
     68m2

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    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.
    Search in sidebar queryNow, 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× 2.25 m
    Area of rectangle EFIJ = 19.125m2
    We know that,
    Area of rectangle LKGH = Area of rectangle EFIJ
    Area of rectangle LKGH = 19.125m2
    Area of rectangle DIKC = DI ✕IK = 2.25 m × 5.5 m
    Area of rectangle DIKC = 12.375m2
    We know that,
    Area of rectangle JABL = Area of rectangle DIKC
    Area of rectangle JABL = 12.375m2
    Now,
    Area of the verandah = 19.125 + 19.125 + 12.375 + 12.375
    Area of the verandah =63m2
    Hence, the area of verandah is 63m2.
     
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