Two cross roads, each of width 10 m, cut at right angles through the centre of a
rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the
area of the roads. Also find the area of the park excluding cross roads. Give the
answer in hectares.
Answers
Here, PQ=10m and PS=300m, EH=10m and EF=700m
And KL=10m and KN=10m
Area of roads = Area of PQRS+Area of EFGH−Area of KLMN
[∵ KLMN is taken twice, which is to be subtracted]
=PS×PQ+EF×EH−KL×KN
=(300×10)+(700×10)−(10×10)
=3000+7000−100
=9,900m
2
Area of road in hectares, 1m
2
=
10000
1
hectares
∴9,900m
2
=
10000
9900
=0.99 hectares
Now, Area of park excluding cross roads = Area of park−Area of road
=(AB×AD)−9,900
=(700×300)−9,900
=2,10,000−9,900
=2,00,100 m
2
=
10000
200100
hectares=20.01 hectares
Answer:
Explanation: Length of the road parallel to the length of the park = 700 m
Width of the road = 10 m
∴ Area of the road = l × b = 700 m × 10 m = 7000 m2
Length of the road parallel to the breadth of the park = 300 m
Width of the road = 10 m Area of this road = l × b = 300 m × 10 = 3000 m2
Area of the both roads
= 7000 m2 + 3000 m2 – Area of the common portion
= 10,000 m2 – 10 m × 10 m
= 10,000 m2 – 100 m2
= 9900 m2 = 0.99 ha
Area of the park = l × b
= 700 m × 300 m = 210000 m2
Area of the park excluding the roads
= 210000 m2 – 9900 m2
= 200100 m2 = 20.01 ha
hope it helped