Question

find the area of a square whose diagonal length is 4.6​

Answer 1

Here we have to find out the area of a square.

The length of the diagonal is 4.6

We will use this data to find out the side of the square

The relation between the side and diagonal of the square is

$Diagonal = \sqrt{2} side\\Side = \frac{diagonal}{\sqrt{2} } \\ = \frac{4.6}{\sqrt{2} } \\\\ = 3.25$

Now, area of square = side × side

                                  = 3.25 × 3.25

                                  = 10.5625

The area of the square will be 10.5625 square units.

Answer 2

Given: The diagonal length is $4.6$cm.

We have to find the area of a square.

As we know that the area of the square is equal to the$side^{2}$ of the square.

Therefore,

$\begin{array}{l}A=a^{2} \\d=\sqrt{2} a\end{array}$

We are solving in the following way:

We have,

The diagonal length of the square is $4.6$cm.

Solving for $A:$

$=>A=\frac{1}{2} d^{2}\\\\=>A=\frac{1}{2} \times 4.6^{2} \approx 10.58$

Solving the above equation further we get,

$A=$ $10.58$$cm^{2}$

Hence, The area of the square will be $10.58$$cm^{2}$