A lawn50m.long and40m.broad has a path of uniform width 8m. outside it.Find the area of the path.
subtract the area of the lawn from the total area including path:
(50+16)(40+16)-50*40 = ?
1696
To find the area of the path, you need to calculate the difference between the areas of the outer rectangle and the inner rectangle.
The outer rectangle's length will be the original lawn's length plus twice the width of the path on each side, and the breadth will be the original lawn's breadth plus twice the width of the path on each side.
Length of outer rectangle: 50m + 2(8m) + 2(8m) = 50m + 16m + 16m = 82m
Breadth of outer rectangle: 40m + 2(8m) + 2(8m) = 40m + 16m + 16m = 72m
Therefore, the area of the outer rectangle is: 82m x 72m = 5,904m²
The inner rectangle's length will be the original lawn's length, and the breadth will be the original lawn's breadth.
Length of inner rectangle: 50m
Breadth of inner rectangle: 40m
Therefore, the area of the inner rectangle is: 50m x 40m = 2,000m²
Finally, subtract the area of the inner rectangle from the area of the outer rectangle to find the area of the path.
Area of path = Area of outer rectangle - Area of inner rectangle
Area of path = 5,904m² - 2,000m²
Area of path = 3,904m²
Therefore, the area of the path is 3,904 square meters.
To find the area of the path around the lawn, you can subtract the area of the inner rectangle (lawn) from the area of the outer rectangle (total area with the path). Here's how you can do it step by step:
1. Find the area of the inner rectangle (lawn):
- Length = 50m
- Width = 40m
Area of the lawn = Length * Width = 50m * 40m = 2000 square meters
2. Find the dimensions of the outer rectangle (total area with the path):
- Since the path has a uniform width of 8m on each side, you need to add 8m to the length and width of the lawn on each side.
- Length = 50m + 2 * 8m = 66m (added 2*8m because path is on both sides)
- Width = 40m + 2 * 8m = 56m (added 2*8m because path is on both sides)
3. Find the area of the outer rectangle:
Area of the outer rectangle = Length * Width = 66m * 56m = 3696 square meters
4. Finally, calculate the area of the path:
Area of the path = Area of the outer rectangle - Area of the inner rectangle
Area of the path = 3696 square meters - 2000 square meters = 1696 square meters
Therefore, the area of the path is 1696 square meters.