Question

A cube has a surface area of 486 cm2. What is the side length ?

Answer 1

a Cube, has all equal sides, namely, the length, width and height
are all equal to each other

so.. notice the picture added here
you have really, 6 squares, stacked up to each other at the edges

so...what is the Area of one of those squares?
well, if the sides are equal, let's say the side is "x" long, then
the Area is
`x\cdot x \implies x^2`

well, you have 6 of those squares, thus
`\bf \textit{surface area of a cube}= \begin{cases} (x\cdot x)+\\ (x\cdot x)+\\ (x\cdot x)+\\ (x\cdot x)+\\ (x\cdot x)+\\ (x\cdot x)\\ --------------\\ x^2+x^2+x^2+x^2+x^2\\ 6x^2 \end{cases} \\\\ \textit{we know the Area is }486\ cm^2\qquad thus \\\\ \textit{surface area}=6x^2\implies 486=6x^2`

solve for "x", to get one side's length