I cannot seem to comprehend why the dimensions of area are length squared. Area is the number of square units in a plane surface and is measured in terms of squares of sides of unit length. In short , I cannot fathom the meaning of a length times a length. Please shed some light on the matter .
[Math] Area dimensions
dimensional analysis
Best Answer
In terms of "visually" seeing why using algebra, consider the following example...
To calculate the area of a triangle with $b = 3 \text{ in}$ and $h = 4 \text{ in}$, then the formula for area of a triangle is $$\begin{align}A_\triangle & = {1 \over 2}bh \\ & = {1 \over 2}(3 \text{ in})(4 \text{ in}) \\ & = {1 \over 2}(3)(4)\text{ in} \times \text{in} \\ & = 2(3)(\text{in})^2 \\ & = 6 \text{ in}^2\end{align}$$
You could apply this argument for any dimension of length.