Two cross roads, each of width 5m, run at right angles through the cen

1.	Two cross roads, each of width 5m, run at right angles through the centre of a rectanglepark of lengths 70m and breadth 45m and parallel to its sides. Find the area of the roads.
Answer» $\large\underline{\bf{Solution-}}$ GIVEN that, RECTANGULAR Park = ABCD Longer Path = EFGH Shorter Path = PQRS Common Path = WXYZ Dimensions of FIELD are $\rm :\longmapsto\:Length \: of \: rectangular \: park, \: l \: = \: 70 \: m$ $\rm :\longmapsto\:Width \: of \: rectangular \: park, \: b \: = \: 45 \: m$ $\red{\rm :\longmapsto\:Length \: of \: the \: shorter \: path, \: l_1=45 \: m}$ $\red{\rm :\longmapsto\:Breadth \: of \: the \: shorter \: path, \: b_1=5 \: m}$ $\blue{\rm :\longmapsto\:Length \: of \: the \: longer \: path, \: l_2=70 \: m}$ $\blue{\rm :\longmapsto\:Breadth \: of \: the \: longer \: path, \: b_2=5 \: m}$ Consider, $\red{\bf :\longmapsto\:Area \: of \: shorter \: path, \: A_1=l_1×b_1}$ $\rm :\longmapsto\:A_1 = 45 \times 5$ $\red{\bf :\longmapsto\:A_1 = 225 \: {m}^{2}}$ Consider, $\blue{\bf :\longmapsto\:Area \: of \: longer \: path, \: A_2=l_2×b_2}$ $\rm :\longmapsto\:A_2 = 70 \times 5$ $\blue{\bf :\longmapsto\:A_2 = 350\: {m}^{2}}$ Thus, Area of path (P) is given by, $\green{\bf :\longmapsto\:P=A_1+A_2−Area \: of \: common \: path}$ $\rm :\longmapsto\:P=225 + 350 - 5 \times 5$ $\rm :\longmapsto\:P=575 - 25$ $\green{\bf :\longmapsto\:P = 550 \: {m}^{2}}$ ADDITIONAL INFORMATION :- $\boxed{ \sf \: Area_{(rectangle)} = length \times breadth}$ $\boxed{ \sf \: Area_{(square)} = {(side)}^{2}}$ $\boxed{ \sf \: Area_{(rhombus)} = base \times height}$ $\boxed{ \sf \: Area_{(parallelogram)} = base \times height}$ $\boxed{ \sf \: Area_{(circle)} = \pi {r}^{2} }$