Question

by splitting the figure into rectangles, find its area

Answer 1

We know that, In Rectangle Opposite sides are equal.

Taking the First Rectangule as ABCJ,

(Refer the attachment for the figure)

As Opposite sides are equal,

$\sf{AB\:=\:JC\:and\:BC\:=\:AJ}$

$\sf{4\:=\:3\:+\:x\:and\:2\:+\:x\:=\:3}$

To make both equal, 'x' must be 1.

Substituting values, we get,

$\implies\sf{4\:=\:3\:+\:x\:and\:2\:+\:x\:=\:3}$

$\implies\sf{4\:=\:3\:+\:1\:and\:2\:+\:1\:=\:3}$

$\implies\sf{4\:=\:4\:and\:3\:=\:3}$

Hence, Length = 4 and breadth = 3

Taking the second Rectangle as DIHE :

(Refer the attachment for the figure)

As Opposite sides are equal,

$\sf{DE\:=\:IH\:and\:DC\:=\:EH}$

Substituting values, we get,

$\implies\sf{3\:+\:x\:=\:4\:and\:2\:+\:x\:=\:EH}$

$\implies\sf{\:3\:+\:1\:=\:4\:and\:2\:+\:1\:=\:EH}$

$\implies\sf{4\:=\:4\:and\:3\:=\:3}$

Hence, Length = 4 and breadth = 3

Taking the Third Rectangle as FEHG :

(Refer the attachment for the figure)

As Opposite sides are equal,

$\sf{FE\:=\:GH\:and\:FG\:=\:EH}$

We know that, EH = 3

If EH = 3, FG = 3

FE = 4, and GH is also = 4

Hence, Length = 4 and breadth = 3

From this,

All the three Rectangle states that,

• Length = 4 cm
• Breadth = 3 cm

Formula to find area :

$\boxed{Area\:of\:a\:Rectangle\:=\:Length\:×\:Breadth}$

Substituting values we get,

$\implies\sf{Area\:=\:4\:×\:3}$

$\implies\sf{Area\:=\:7\:cm^2}$

Therefore, the area of the rectangle = 7 cm².