Question

A path of uniform width 4 m runs around the outside of a rectangular field 24 m by 18 m. Find the area of the path.

Answer 1

Hint: We are given a rectangular field with its dimension and are asked to find the area of a uniform path of width 4 m around it. To obtain this we will draw the geometry first and will do certain algebraic operations to find the required area. The formula for area of the rectangle will help us throughout the solving procedure.
The area of a rectangle of length ‘l’ and breadth ‘b’ is $ l \times b $ .

Complete step-by-step answer:

Let’s first draw the situation geometrically.
We have a rectangular field of dimensions 24 m and 18 m. We will name it ABCD.
We are also given a path of 4 m that runs around the given rectangle ABCD. So we will draw another rectangle PQRS of dimensions increased by 4 m on each side which gives a dimension of (24+4+4) m and (18+4+4) m.
Now the figure below is the required one for us.
For a better convenience we have colored the rectangles.
“Blue+Red” for PQRS and “Red” for ABCD.
We are asked to find the area of the blue region only.
This can be achieved by finding the area of the larger rectangle PQRS and then subtracting the area of the smaller rectangle ABCD to it.
Required area=Area of PQRS-Area of ABCD --(1)
In rectangle PQRS we have,
l=24+4+4=32 m and b=18+4+4=26 m
So,
Area of PQRS $ = 32 \times 26 = 832 $ sq. m --(2)
In rectangle ABCD we have,
l=24 m and b=18 m
So,
Area of PQRS $ = 24 \times 18 = 432 $ sq. m --(3)
Putting values from (2) and (3) in (1) we get:
Required area=832 sq. m – 432 sq. m=400 sq. m
Hence our required area is 832 sq. m
Therefore, the area of a 4 m path around a rectangular field of dimensions 24 m by 18 m is 832 sq. m
So, the correct answer is “832 sq. m”.

Note: Always draw the geometry as asked in the question as it gives a clear picture of what is asked and what is needed to be calculated. Write the units of measurement after finding the answer. The unit of length is cm,m,km,etc while the unit of area is sq. cm, sq. m, sq. km,etc