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Question

Length and breadth of rectangle ABCD are l cm and b cm respectively. If width of green coloured path is w cm, then which of the following represents brown coloured area
  1. (l+bw)w
  2. lb(l+bw)w
  3. lb+(l+bw)w
  4. lb(l+b+w)w


Solution

The correct option is B lb(l+bw)w
Given : AB=CD = l cm, BC=AD = b cm.
     EF=IJ=LK=GH=MN=OP=MP=ON= w cm.

Area of rectangle ABCD
       = length×breadth = l×b = lb cm2

Area of rectangle EFJI
      = breadth×width = b×w = bw cm2

Area of rectangle LGHK
      = length×width = l×w = lw cm2

Area of square MNOP
     = side2MN2w2 cm2

Brown coloured area 
= Area of rectangle ABCD - Area of green colored path
= Area of rectangle ABCD
 - (Area of rectangle EFJI + Area of rectangle LGHK - Area of square MNOP)
lb(bw+lww2)
=  lb(l+bw)w

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