Question

Daya walks 3 km south. He then takes the following directions in the same order: -
(i) 5 km towards the East
(ii) 3 km towards the North
(iii) 5 km towards the West
What is the area of the shape in square km made upon completing the journey?

Answer 1

Hint: First of all find the polygon due to the path followed by Daya while walking and before completing the journey. The polygon will be a rectangle. Now, use the formula for the area of a rectangle given as $A=l\times b$ to get the answer. Here A is the area of the rectangle, l is its length and b is its breadth. Substitute the values l = 5 km and b = 3 km.

Complete step by step answer:
Here we have been asked to find the area of the polygon that will be formed by Daya before completing the journey through the path provided in the question. Let us first try to find the polygon by tracing Daya’s path.
Now, the journey is in four parts they are: -
(1) He walks 3 km south
(2) 5 km towards the east
(3) 3 km towards the north
(4) 5 km towards the west
Let us assume that he started from the point P so we have the following path followed by him.

Clearly we can see that the path of the journey is a rectangle and we know that the area of a rectangle is given as $A=l\times b$, where A is the area of the rectangle, l is its length and b is its breadth. Substituting the values l = 5 km and b = 3 km we get,
\[\begin{align}
  & \Rightarrow A=5\times 3 \\
 & \therefore A=15k{{m}^{2}} \\
\end{align}\]
Hence, the area of the shape made upon completing the journey is 15 square kilometer.

Note: It is necessary to draw the diagram of the path followed because if we do not have the shape then it will not be possible to find the area of the figure that is being made. Remember all the four directions carefully although it is not of much importance here but in certain questions if the directions taken will be wrong then the resultant figure and hence the answer will be wrong.