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 Anp+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