丸い and 四角い: round and four-sided shapes
Describe round and four-sided objects, without assuming that 四角い always specifies a perfect square.
The shape of round objects
丸い皿に果物を盛りました。 says that someone served fruit on a round plate. 丸い, read まるい, describes a rounded shape without prominent corners.
丸いボールを転がしました。 says that someone rolled a round ball. 丸い applies to rounded three-dimensional objects as well as flat circular shapes.
The scope of four-sided shapes
四角い箱を棚に置きました。 says that someone put a box with a four-sided shape on a shelf. 四角い, read しかくい, does not by itself specify equal side lengths.
この紙は四角いですが、正方形ではありません。 says that the paper is four-sided but not square. For precise geometry, specify 正方形 or 長方形.
Describe making a shape
生地を丸く伸ばしてください。 asks someone to roll the dough out into a round shape. 丸く describes the resulting shape, unlike 丸い生地 modifying a noun.
紙を四角く切りました。 says that someone cut paper into a four-sided shape. A task requiring exact dimensions or angles needs those details added.
Does 四角い紙 alone establish four equal sides?
Show the answer and why
No. It describes a four-sided shape, not necessarily a perfect square. Specify 正方形 when that distinction matters.