ABCD is a rectangular park of measures (a × b) and let there be a path of uniform width 'c' all around the park. Find the area of the path
area of ABCD = ab
area of ABCD+path = (a+2c)(b+2c)
area of path = (a+2c)(b+2c)-ab
To find the area of the path, we need to subtract the area of the inner rectangle (ABCD) from the area of the outer rectangle including the path.
The outer rectangle of the path can be formed by extending each side of the inner rectangle (ABCD) with a distance equal to the width of the path (c). Therefore, the dimensions of the outer rectangle are (a + 2c) × (b + 2c).
To calculate the area of the path, we subtract the area of the inner rectangle from the area of the outer rectangle:
Area of the path = Area of the outer rectangle - Area of the inner rectangle
Area of the outer rectangle = (a + 2c) × (b + 2c)
Area of the inner rectangle = a × b
So the area of the path is:
Area = (a + 2c) × (b + 2c) - a × b
This formula allows you to calculate the area of the path in terms of the dimensions of the park (a and b) and the width of the path (c).