A rectangular field 50 m long and 42 m wide consists of a rectangular lawn inside. It is surrounded by a gravel path of uniform width. If the width of the path is 6 metres, then the area of the path is

Given:
Length of the rectangular field = 50 m
Width of the rectangular field = 42 m
Width of the path = 6 m

Concept -

Area of the larger rectangle (field) = Length × Width

Area of the path = Area of the field - Area of the lawn

Explanation -

Area of the field = 50 m × 42 m = 2100 square meters

Now, let's calculate the area of the lawn inside the field:
Length of the lawn = Length of the field - 2 x width of the path (since the path surrounds the lawn on both sides)
Width of the lawn = Width of the field - 2 x width of the path

Length of the lawn = 50 m - 2 x 6 m = 50 m - 12 m = 38 m
Width of the lawn = 42 m - 2 x 6 m = 42 m - 12 m = 30 m

Area of the lawn = Length of the lawn × Width of the lawn
Area of the lawn = 38 m × 30 m = 1140 square meters

Now, the area of the path surrounding the lawn is the difference between the area of the field and the area of the lawn:

Area of the path = Area of the field - Area of the lawn
Area of the path = 2100  - 1140  = 960 square meters

Therefore, the area of the path surrounding the lawn inside the rectangular field is 960 square meters.