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.

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:**

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 m^{2}

Inner area of garden without path = length * breadth = 90 * 75 = 6,750 m^{2}

Now, Area of path = Area of garden with path – Area of garden without path

= 8,500 – 6,750

= 1,750 m^{2}

Since, 1 m^{2} = 1/10000 hectares

Therefore, 6,750 m^{2} = 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:**

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 m^{2}

Area of road in hectares, 1 m^{2} = 1/10000 hectares

So, 9,900 m^{2} = 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 m^{2}

= 200100/10000 hectares

= 20.01 hectares

.