question_answer 39)

Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of the length 700 m and the breadth 300 m parallel to its sides. Find the area of the roads. Also find the area of park excluding cross roads. Give the answer in hectare.

Answer:

                Area of the roads = Area of the rectangle PQRS + Area of the rectangle EFGH ? Area of the square KLMN \[=(\text{3}00\times \text{1}0+\text{7}00\times \text{1}0-\text{1}0\times \text{1}0)\text{ }{{\text{m}}^{\text{2}}}\] \[=(\text{3}000+\text{7}000-\text{1}00)\text{ }{{\text{m}}^{\text{2}}}=\text{999}0\text{ }{{\text{m}}^{\text{2}}}\] or  \[=\frac{9900}{10000}=0.99\,ha\].      Area of the rectangle \[\text{ABCD }=l\text{ }\times \text{ }b\text{ = 700 m  }\!\!\times\!\!\text{  300 m = 210000 }{{\text{m}}^{\text{2}}}\] \[\therefore \] Area of the park excluding cross roads = Area of the rectangle ABCD ? Area of the roads    \[\text{= 210000 }{{\text{m}}^{\text{2}}}\text{- 9990 }{{\text{m}}^{\text{2}}}\text{= 200010 }{{\text{m}}^{\text{2}}}\] \[\text{=}\frac{200010}{10000}\text{ hectar}=20.00\text{1 hectare}\text{.}\]