A rectangular lawn is 50 m long and 30 m wide it has roads 2 m wide joining the mid points of opposite sides and also a path of same breadth is running along inside the lawn what is the total area of roads and paths
draw a diagram. It will show 4 identical rectangular areas that are not paved. Find the area of one of those, multiply by 4, and subtract that from the total 1500m^2 area.
That will be the area of the paved parts.
To find the total area of the roads and paths, we first need to determine their individual areas and then add them together.
1. Area of the roads:
The roads are 2 m wide and join the midpoints of opposite sides of the rectangular lawn. Therefore, there are two roads that are parallel to the longer sides of the lawn. Each road's length is the same as the width of the lawn (30 m), and its width is 2 m.
So, the total area covered by the roads can be calculated as:
Area of one road = length × width = 30 m × 2 m = 60 m²
Since there are two road sections (one on each end), the total area of the roads is:
Total area of roads = 2 × Area of one road = 2 × 60 m² = 120 m²
2. Area of the inner path:
The inner path is also 2 m wide, and it runs along the inside perimeter of the lawn. To calculate its area, we need to find the length and width of the path.
The length of the inner path (remaining after deducting the width of the roads) is:
Length of inner path = Length of lawn - 2 × Width of road = 50 m - (2 m × 2) = 50 m - 4 m = 46 m
The width of the inner path remains the same as the width of the lawn, which is 30 m.
So, the area covered by the inner path is:
Area of inner path = length × width = 46 m × 30 m = 1380 m²
Now, to find the total area of the roads and paths:
Total area = Area of roads + Area of inner path = 120 m² + 1380 m² = 1500 m²
Therefore, the total area of the roads and paths is 1500 square meters.