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:

Let's represent the situation using a diagram as shown below.

Let the blue region represent the park and the orange region represent the roads.

Area of the park = Length × Breadth

= 700 m × 300 m

= 210000 m²

Length of the road parallel to the length of the park = 700 m

Width of the road = 10 m

Area of the road ABDC = Length × Breadth

= 700 m × 10 m

= 7000 m²

Length of the road parallel to the breadth of the park = 300 m

Width of the road = 10m

Area of road EFGH = Length × Breadth

= 300 m × 10 m

= 3000 m²

Note that IJLK  is a common region between the two roads which is a square with a side length of 10 m.

Therefore, area of both the roads = Area of the road ABDC + Area of road EFGH - Area of Common Portion IJLK

= 7000 m² + 3000 m² - (10 ×10) m²

= 10000 m² - 100 m²

= 9900 m²

= 0.99 hectares

Therefore, area of the park excluding the roads = Area of the Park - Area of the roads

= 210000 m² - 9900 m²

= 200100 m²

= 20.01 hectares

☛ Check: NCERT Solutions for Class 7 Maths Chapter 11

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Video Solution:

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

Maths NCERT Solutions Class 7 Chapter 11 Exercise 11.4 Question 6

Summary:

Two cross roads, each of width 10 m, cut a right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. 0.99 hectares is the area of the roads. Also 20.01 hectares is the area of the park excluding cross roads.

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