Question

Two cross roads, each of width 5m, run at right angles through the centre of a rectangle
park of lengths 70m and breadth 45m and parallel to its sides. Find the area of the roads.
​

Answer 1

FINAL ANSWER:-

area of the roads ⇒ $550m^{2}$

TO FIND:-

the area of the roads

GIVEN:-

Two cross roads, each of width⇒ 5 m

length of first parallel road ⇒ 70 m

breadth of park ⇒ 45m

FORMULA USED:-

area of rectangle = Length × Breadth

SOLUTION:-

area of first road = 70×5 ⇒ $350m^{2}$

length of second road = 45 m

area of second road = 45×5 ⇒ $225 m^{2}$

area of the common part of cross road with 5 m width that  lies at the center of the park = 5×5 ⇒ $25 m^{2}$

area of roads = area of first road + area of second cross road−common area

$=(350+225)-25\\=575-25\\=550m^{2}$      

================================================================                                      

Answer 2

$\large\underline{\bf{Solution-}}$

Given that,

• Rectangular Park = ABCD

• Longer Path = EFGH

• Shorter Path = PQRS

• Common Path = WXYZ

Dimensions of field are

$\rm :\longmapsto\:Length \: of \: rectangular \: park,  \: l \: = \: 70 \: m</p><p>$

$\rm :\longmapsto\:Width \: of \: rectangular \: park, \: b \: = \: 45 \: m$

$\red{\rm :\longmapsto\:Length \: of \: the \: shorter \: path,  \: l_1=45 \: m}$

$\red{\rm :\longmapsto\:Breadth \: of \: the \: shorter \: path,  \: b_1=5 \: m}$

$\blue{\rm :\longmapsto\:Length \: of \: the \: longer \: path,  \: l_2=70 \: m}$

$\blue{\rm :\longmapsto\:Breadth \: of \: the \: longer \: path,  \: b_2=5 \: m}$

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 :-

$\boxed{ \sf \: Area_{(rectangle)} = length \times breadth}$

$\boxed{ \sf \: Area_{(square)} = {(side)}^{2}}$

$\boxed{ \sf \: Area_{(rhombus)} = base \times height}$

$\boxed{ \sf \: Area_{(parallelogram)} = base \times height}$

$\boxed{ \sf \: Area_{(circle)} = \pi {r}^{2} }$