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

• A. $lb+(l+b-w)w$
• B. $lb-(l+b+w)w$
• C. $(l+b-w)w$
• D. $lb-(l+b-w)w$

Answer 1

The correct option is D $lb-(l+b-w)w$

Given : AB=CD = $l$ cm, BC=AD = $b$ cm.
EF=IJ=LK=GH=MN=OP=MP=ON= $w$ cm.

Area of rectangle ABCD
= length$\times$breadth = $l$$\times$$b$ = $lb$ $c{m}^2$

Area of rectangle EFJI
= breadth$\times$width = $b$$\times$$w$ = $bw$ $c{m}^2$

Area of rectangle LGHK
= length$\times$width = $l$$\times$$w$ = $lw$ $c{m}^2$

Area of square MNOP
= $sid{e}^2$ = $M{N}^2$ = $w^2$ $c{m}^2$

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)
= $lb-(bw+lw-w^2)$
= $lb-(l+b-w)w$