das Quadrat
square
In geometry, a flat shape with four sides of equal length and four right angles.
Der Lehrer zeichnete ein Quadrat an die Tafel.
The teacher drew a square on the board.

square
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square
In geometry, a flat shape with four sides of equal length and four right angles.
Der Lehrer zeichnete ein Quadrat an die Tafel.
The teacher drew a square on the board.

You can recognize the meaning from the context. If it is about shapes and drawing, the geometric figure is meant. In connection with numbers, it refers to the second power. With fabrics or surfaces, it refers to a pattern.
Das Quadrat von 5 ist 25.
The square of 5 is 25.
'Quadrat' (square) is a common component of compound words that describe an area. The best-known example is 'der Quadratmeter' (square meter, m²), a unit of measurement for areas.
Die Wohnung hat eine Fläche von 80 Quadratmetern.
The apartment has an area of 80 square meters.
When it comes to mathematics, 'Quadrat' (square) is almost always used with the preposition 'von' to indicate the base. The fixed structure is: das Quadrat von + number.
Was ist das Quadrat von 12?
What is the square of 12?
In the context of patterns and designs, the plural 'Quadrate' (squares) is often used. Typical phrases are 'ein Muster aus Quadraten' (a pattern of squares) or 'in Quadrate unterteilt' (divided into squares).
Das Schachbrett besteht aus schwarzen und weißen Quadraten.
The chessboard consists of black and white squares.
triangle
'das Dreieck' and 'das Quadrat' are both geometric shapes, so learners may confuse them when learning shapes. The most important difference is the number of sides and corners. A 'Dreieck' has three sides and three corners. A 'Quadrat' has four sides of equal length and four right angles. If it is only about a shape with three corners, 'Dreieck' is the right word. If all four sides are the same length and the corners form right angles, 'Quadrat' is the right word.

Im Unterricht malt ihr ein Quadrat und messt danach alle vier Seiten.
In class, you draw a square and then measure all four sides.
Für das Schild schneidet Mehmet ein rotes Dreieck aus Papier aus.
For the sign, Mehmet cuts a red triangle out of paper.