四角と正方形はどう違うの？~(What's the difference between 四角 and 正方形?)

Question

While going through one of my study sets I created back in December containing words only marked as N2, I came across [正方形]{せいほうけい}, which was translated as "square". However, I always was taught and remember [四角]{しかく} to mean "square", so my question is, what's the difference?

Answer 1

They are used in different contexts with different but overlapping meanings.

• 正方形 is a mathematical term for a square (a polygon with four sides of equal length and four angles of 90 degrees).
• 四角 is a daily-use word for a quadrilateral (a polygon with four sides), and we never use it in mathematics (unless it is part of a compound word). However, in the daily language, often we do not make a distinction between the case where we mean a quadrilateral in general and the case where we mean a more specific kind of quadrilateral. Therefore, we often just say 四角 when we mean a square. This is probably why you were taught that 四角 means a square.

There is also a word 四角形.

• 四角形 is a mathematical term for a quadrilateral. But when it is used in the daily language, 四角形 is just a little more formal version of 四角, and it does not necessarily mean a general quadrilateral.

The difference between 四角 and 四角形 is analogous to that between 三角 and 三角形: What's the difference between 三角 and 三角形?

Answer 2

四角 is a diagram which is framed in by four lines on flat, so oblong figure and trapezoid are 四角.

正方形 is a kind of 四角 and it's called "square" in English. It is framed in by four same lines and angles.