|Class 7 Maths Perimeter and Area||Applications|
We have seen in gardens or parks, some space is left all around in the form of path or in between as cross paths as shown in the figure.
We need to find the areas of such pathways or borders when we want to find the cost of making them.
Problem: A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectares.
Length of rectangular garden = 90 m and breadth of rectangular garden = 75 m
Outer length of rectangular garden with path = 90 + 5 + 5 = 100 m
Outer breadth of rectangular garden with path = 75 + 5 + 5 = 85 m
Outer area of rectangular garden with path = length * breadth = 100 * 85 = 8,500 m2
Inner area of garden without path = length * breadth = 90 * 75 = 6,750 m2
Now, Area of path = Area of garden with path – Area of garden without path
= 8,500 – 6,750
= 1,750 m2
Since, 1 m2 = 1/10000 hectares
Therefore, 6,750 m2 = 6750/10000 = 0.675 hectares
Hence, the area of the garden is 0.675 hectares.
Problem: 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.
Here, PQ = 10 m and PS = 300 m, EH = 10 m and EF = 700 m
And KL = 10 m and KN = 10 m
Area of roads = Area of PQRS + Area of EFGH – Area of KLMN
[Since KLMN is taken twice, this is to be subtracted]
= PS * PQ + EF * EH – KL * KN
= (300 * 10) + (700 * 10) – (10 * 10)
= 3000 + 7000 – 100
= 9,900 m2
Area of road in hectares, 1 m2 = 1/10000 hectares
So, 9,900 m2 = 9900/10000 = 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 m2
= 200100/10000 hectares
= 20.01 hectares