Question

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

• A. $np+mp+nq+mq$
• B. $pq+mn+mn+qp$
• C. $(n+p)\times (m+q)$

Answer 1

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

$=length\times breadth$
$=n\times p$
$=np$

• Area of the rectangle with sides $m$ units and $p$ units

$=length\times breadth$
$=m\times p$
$=mp$

• Area of the rectangle with sides $n$ units and $q$ units

$=length\times breadth$
$=n\times q$
$=nq$

• Area of the rectangle with sides $m$ units and $q$ units

$=length\times breadth$
$=m\times q$
$=mq$
$\Rightarrow$ Summing areas of all the smaller rectangles we get,
area of whole rectangle
$=(np+mp+nq+mq)$ unit${}^2$

Method 2: Again we know that length of the larger rectangle $=n+m$,
and breadth of the larger rectangle $=p+q$ units
Hence, area $=(n+m)\times (p+q)$ units
$\therefore \text{Area}=(np+mp+nq+mq)$ unit${}^2$