Class 7 Maths Perimeter and Area Applications

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.

      Class_7_Maths_Perimeter_And_Area_Applications                                                   

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.

Solution:

        Class_7_Maths_Perimeter_And_Area_Garden                                        

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.

Solution:

Class_7_Maths_Perimeter_And_Area_Two_Cross_Roads

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

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