Question

The length of a rectangular park is 700 m and its breadth is 300 m. Two crossroads, each
of width 10 m, cut the centre of a rectangular park and are parallel to its sides. Find the
area of the roads. Also, find the area of the park excluding the area of the crossroads.

Answer 1

$\\ ☆ \: \pink{ \sf \large \underline{ \: Required \: Question:- }}$

The length of a rectangular park is 700 m and its breadth is 300 m. Two crossroads, each of width 10 m, cut the centre of a rectangular park and are parallel to its sides. Find the area of the roads. Also, find the area of the park excluding the area of the crossroads.

$\\ ☆ \: \pink{ \sf \large \underline{ \: SolutiOn :- }}$

★ Here we have given that , $\rm { PQ = 10cm}$

$\\ \sf \: PS = 300m, \: EH = 10m,\: EF = 700m,\: KL = 10m$

$\\ \sf \green {\: Area \: of \: roads \: = Area \: of \: PQRS + Area \: of \: EFGH - Area \: of \: \: KLMN \:}$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: PS \times PQ + EF \times EH - KL \times KN$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: (300 \times 10) + (700 \times 10) - (10 \times 0) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \sf \: 3000 + 7000 - 100 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \sf \implies \boxed{ \underline\frak \pink{9900m^{2} }}$

Area of roads in Hectors ,

We know that, $\sf 1 {m}^{2} = \frac{1}{10000} \: hectors$

$\\ \sf \: \: \: \: \therefore \:9900 {m}^{2} = \frac{9900}{10000} = \bold{0.99 \: hectares}$

$\\ \sf \: Now, \\ \\ \sf \: \: \: \: \: \: \: \green{ Area \: of \: part \: excluding \: cross \: roads \: = \: Area \: of \: part \: - \: Area \: of \: Road }$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: (AB \times AD) - 9900$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: (700\times 300) - 9900$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 210000 - 9900$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \boxed{ \underline \frak \blue{ 200100 \: {m}^{2}}}$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \frac{200100 \: {m}^{2} }{10000} \: hectares$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \boxed{ \underline \frak \pink{ 20.01 \: hectares}}$

$\\ \sf \underline { \: \: \: Area \: of \: part \: excluding \: cross \: roads \: \: is \underline \bold{\: 20.01 \: hectares \: } \: \: }.$