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To find the area, we multiply the base and height for a parallelogram, in the case of a square. Both base and height are equal to each other. So we will do $\text{side }\!\!\times\!\!\text{ side}$ .

The given sides of the square are $18x-20$ and $42-13x$. According to the definition of the square, all four sides of the square are equal.

So we can equate two sides of a square.

Hence it can be written as

$\Rightarrow 18x-20=42-13x$

On collecting like terms

\[\Rightarrow 18x+13x=42+20\]

\[\Rightarrow 31x=62\]

\[\Rightarrow x=2\]

On substituting $x=2$ in given sides of the square.

At $x=2$, value of $18x-20$ is calculated below

\[\Rightarrow 18\times 2-20\]

$\Rightarrow 36-20$

$\Rightarrow 16$

At $x=2$, value of $42-13x$

\[\Rightarrow 42-13\times 2\]

\[\Rightarrow 42-26\]

\[\Rightarrow 16\]

If the side of the square is a then area(A) of the square is

$\Rightarrow A=a\times a$

$\Rightarrow A={{a}^{2}}$

In the given question the side of the square is 16.

Required area is

$\Rightarrow A={{\left( 16 \right)}^{2}}$

$\Rightarrow A=256\,\text{square}\,\text{units}$.