Question

If the length of a rectangle is $2.1\;m$ and width is \[1.62\;m\;\] then its area will be
A. $3.402\;{m^2}$
B. $3.4\;{m^2}$
C. $3.40\;{m^2}$
D. $3\;{m^2}$

Answer 1

Hint: Even though a rectangle consists of four sides the length and breadth values are sufficient to calculate the area. The formula for the area of a rectangle in terms of its length and the breadth is applied to find the area. The rule for the significant figures is applied after multiplication in order to determine the correct answer.

Formula used:
The area of a rectangle is given by equation:
$A = l \times b$
Where, $A$ is the area of the rectangle, $l$ is the length of the rectangle and $b$ is the breadth of the rectangle.

Complete step by step answer:
A rectangle is a regular shape that consists of four sides out of which the sides which are greater in magnitude are called the length and the relatively shorter sides are known as the breadth of the rectangle. The lengths of the rectangle are said to be equal and opposite to each other. The rectangle is constructed in such a way that the opposite sides are parallel to each other. The lengths and the breadths are at right angles to each other.

The diagram below illustrates how the shape looks:

Since the lengths of a rectangle are equal and so are its corresponding breadths, the value of one of its lengths and one of its breadths is more than sufficient to calculate the area of the rectangle.

By definition the area of the rectangle indicates the region inside the rectangle or in other words the space enclosed within the boundary of the rectangle which is what we are asked to calculate. The SI unit of area is ${m^2}$. The diagram below shows what the area of the rectangle signifies. The shaded portion of the rectangle ABCD gives the area of the rectangle.

The area is computed using a mathematical formula. It is calculated by multiplying the length of the rectangle by its breadth. Hence it is given by the following equation:
$A = l \times b$ -----($1$)

Let us now extract the data given in the question. The question gives the length and the width of the rectangle. The width is nothing but the breadth of the rectangle.Given, $l = 2.1\;m$ and $b = 1.62\;m$. The units of lengths and breadths are in the correct units, that is the SI units which are meters. Hence the unit for area will be in square meters.Hence we substitute the above values in equation ($1$), we get:
$A = 2.1 \times 1.62$
$ \Rightarrow A = 3.402\,{m^2}$

Now the concept of significant figures comes into picture. There is a rule for the rounding off the number when multiplication operation is performed on two numbers. This rule states the least number of digits are taken to be significant and hence the above answer is rounded to two significant figures. Hence the area becomes:
$ \therefore A = 3.4\;{m^2}$
Hence the area of the rectangle is said to be $3.4\;{m^2}$.

Hence the correct option is option B.

Note: The concept of perimeter of a rectangle is different from the concept of area of the rectangle. The perimeter of the rectangle is concerned with the boundary of the rectangle, that is, the outer region or boundary of the rectangle while the area specifies the region inside the boundary.