Square Area

The area of a square is found by multiplying the length of one side, $l$, by itself. The formula is: $$ A = l \cdot l = l^2 $$

This formula for calculating the area $A$ of a square is derived from the general formula used for rectangles and quadrilaterals, where area is the product of the base $b$ and the height $h$.

$$ A = b \cdot h $$

In a square, since all sides are equal, the base is equal to the height, meaning $l = b = h$.

$$ A = l \cdot l $$

$$ A = l^2 $$

Therefore, the area of a square is simply the square of the length of one of its sides.

The Inverse Formula

To determine the length of a side when the area of the square is known, you can take the square root of the area.

$$ A = l^2 $$

$$ \sqrt{A} = \sqrt{l^2} $$

$$ \sqrt{A} = l $$

Thus, the length of a side of the square is equal to the square root of the area.

$$ l = \sqrt{A} $$

A Practical Example

Consider a square with a side length of 4 cm.

$$ l = 4 \ cm $$

The area of the square is calculated by squaring the length of the side.

$$ A = l^2 $$

$$ A = l \cdot l $$

$$ A = 4 \ cm \cdot 4 \ cm $$

$$ A = 16 \ cm^2 $$

The area of the square is 16 square centimeters.

And so on.