# Why are the formulas for finding area for a square vs. a rectangle different?

I'm puzzled about why the formula for area of a square is side squared, but for a rectangle it's length times height. Why wouldn't it be for a square, side times side?

• It's the smae formula, except width = height = side for squares! – Bernard Oct 8 '17 at 16:31
• In other words, side $\times$ side = side${}^2$. – J.-E. Pin Oct 8 '17 at 16:32
• Actually you can get the area of the square also using the formula for the rhombus $$\frac{diagonal\times diagonal }{2}$$ – Raffaele Oct 8 '17 at 16:38

## 3 Answers

The reason is simple and follows a common tradition in human communication far away from mathematics: We don't say "I ate an apple and an apple", though nothing factually or grammatically wrong. We prefer to say "I ate two apples"

"Side times side" is equal to "side squared". So they are the same. $$\text{side }\times\text{ side} = \text{side}^2$$

I am writing this to answers because I can't write it to the comments Assume that you have a square with side (say) $a$ units long, the area of this square (as we know it) is $a^2$; And then assume that you have pasted two squares horizontally; Now you have o add the area of these two squares $a^2+a^2=2a^2$ which we already knew from $side\times side$, this is a little demonstration of the fact that you can make two squares out of rectangles and add their areas together to prove that the area of a rectangle $=\text{side}\times\text{side}$. And my apologies because I am a beginner in Geogebra.