Question

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. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

Answer 1

The answer is below

Explanation:

The above problem is represented in the image below.

a) To find the area of the cross roads, we use the formula:

Area of cross roads = area of EFGH + area of IJKL - area of PQRS.

Area of rectangle = length * breadth; area of square = length * length

Rectangle EFGH = 300 m by 10 m;

Area of Rectangle EFGH = 300 m * 10 m = 3000 m²

Rectangle IJKL = 700 m by 10 m;

Area of Rectangle EFGH = 700 m * 10 m = 7000 m²

Square PQRS = 10 m by 10 m;

Area of Square PQRS = 10 m * 10 m = 100 m²

Area of cross roads = area of EFGH + area of IJKL - area of PQRS

Area of cross roads = 3000 m² + 7000 m² - 100 m² = 9900 m²

Area of cross roads = 9900 m²

1 hectare = 10000 m². Hence:

Area of cross roads = 9900 m² * (1 hectare / 10000 m²) = 0.99 hectare

Area of cross roads = 0.99 hectare

b) Area of the park excluding cross roads = Area of rectangle ABCD - Area of cross roads

Rectangle ABCD = 700 m by 300 m;

Area of Rectangle ABCD = 700 m * 300 m = 210000 m²

Therefore, substituting:

Area of the park excluding cross roads = 210000 m² - 9900 m² = 200100 m²

Area of the park excluding cross roads = 200100 m² * (1 hectare / 10000 m²)

Area of the park excluding cross roads = 20.01 hectare