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Question

The area of the rectangle in the diagram shown below is .


A
np+mp+nq+mq
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B
pq+mn+mn+qp
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C
(n+p)×(m+q)
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Solution

The correct option is A np+mp+nq+mq

Method 1: Area of the whole rectangle is the sum of area of all 4 smaller rectangles.
  • Area of the rectangle with sides n units and p units
=length×breadth
=n×p
=np
  • Area of the rectangle with sides m units and p units
=length×breadth
=m×p
=mp
  • Area of the rectangle with sides n units and q units
=length×breadth
=n×q
=nq
  • Area of the rectangle with sides m units and q units
=length×breadth
=m×q
=mq
Summing areas of all the smaller rectangles we get,
area of whole rectangle
=(np+mp+nq+mq) unit2

Method 2: Again we know that length of the larger rectangle =n+m,
and breadth of the larger rectangle =p+q units
Hence, area =(n+m)×(p+q) units
Area=(np+mp+nq+mq) unit2

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