Two Cross Roads each of width 10 metre cut at right angles through the
centre of a rectangular Park of 700m and breadth 300m are parallel to its
sides. find the area of the roads also find the area of the park excluding
Crossroads
Answers
Answer:
Step-by-step 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