the length of rectangular park is 700m and its breadth is 400m.2 cross roads each of width 10m,cut the centre of a rectangular park and a parallel to its sides.Find the area of the roads
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Answers
Answer:Area of road = 0.99 hectare, and area of park excluding the roads = 20.01 hectare
Given, Length of the park = 700 m = DC, Width of the park = 300 m = BC, Width of each road = 10m
Let ABCD is a rectangular park. Two roads EFGH and PSRQ is crossing the park at the middle parallel to its side.
Length of Road PSRQ = Width of the park = 300m, Length of the road EFGH = Length of the park = 700m
Area of the rectangular park = Length × Width
= 700 × 300 = 210000 m2 = 21 hectare
Area of Road EFGH = Length × width
= 700m × 10m = 7000m2
Area of Road PSRQ = Length × width
= 300m × 10m = 3000m2
At the crossing of roads; a square KLMN is formed.
The sides of KLMN = Width of the road = 10m
Hence area of KLMN = Side × Side = 10m × 10m = 100m2
As both roads are overlapping each other, so to calculate the area of shaded portion area of one square should be deducted from the area of one of the road.
Hence; Area of cross roads
= Area of one road (PSRQ) + Area of another road(EFGH) — Area of KLMN
= 3000m2 + 7000m2—100m2
= 10000m2 — 100m2 = 9900m2
= 9900 ÷ 10000 = 0.99 hectare
Now, area of park excluding cross roads = Area of park — Areas of cross roads
= 21 hectare —0.99 hectare = 20.01 hectare
Hence, Area of road = 0.99 hectare, and area of park excluding the roads = 20.01 hectare
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