das  Quadrat

A2

Estimated CEFR level.

/kvaˈdʁaːt/

📐 What exactly is a Quadrat?

Das Quadrat (noun, neuter) mainly refers to two things:

• Geometric Shape: A plane *Viereck* (quadrilateral) with four sides of equal length and four right angles (90°). It's a special case of a *Rechteck* (rectangle) and a *Raute* (rhombus).
  Example: Children learn to draw a Quadrat in geometry class.
• Mathematical Term: The result obtained when a number is multiplied by itself (*Potenz* (power) with an exponent of 2).
  Example: The Quadrat of 5 is 25 (5² = 25).

Figuratively, "Quadrat" can also refer to a square-shaped place or area, often in connection with units of area (e.g., Quadratmeter - square meter).

🚨 There is only the article das for this word. Confusion is unlikely.

🧐 Grammar: The Declension of "das Quadrat"

Das Quadrat is a noun with the neuter article das. It is declined as follows:

Singular

Note: In the Genitive and Dative singular, two forms are often possible, with the forms without the additional "e" (Quadrats, Quadrat) being more common.

Plural

Example Sentences 📝

• Nominative: Das Quadrat auf dem Papier ist blau.
  (The square on the paper is blue.)
• Genitive: Die Seitenlänge des Quadrats beträgt 5 cm.
  (The side length of the square is 5 cm.)
• Dative: Mit dem Quadrat kann man gut Flächen berechnen.
  (With the square, one can calculate areas well.)
• Akkusativ: Zeichne bitte das Quadrat fertig.
  (Please finish drawing the square.)
• Plural Nominative: Viele bunte Quadrate schmücken die Wand.
  (Many colorful squares decorate the wall.)
• Plural Dative: In den Quadraten sind Muster versteckt.
  (Patterns are hidden in the squares.)

💡 How to use "das Quadrat"?

Das Quadrat is a commonly used word, especially in contexts related to mathematics, geometry, design, or measurements.

• Geometry & Drawing: When talking about shapes or drawing geometric figures. "Kannst du ein perfektes Quadrat freihändig zeichnen?" (Can you draw a perfect square freehand?)
• Mathematics: When raising numbers to the power of two (squaring). "Das Quadrat von 9 ist 81." (The square of 9 is 81.) We also talk about the Quadratwurzel (square root).
• Area Specifications: Very common in connection with units of measurement like meters, centimeters, etc. "Die Wohnung hat 70 Quadratmeter (m²)." (The apartment has 70 square meters.)
• Everyday Language: Sometimes used metaphorically for something uniform, rigid, or solid. "Er denkt immer nur in seinen festen Quadraten." (He always thinks within his rigid squares - rather rare).
• Art & Design: As a fundamental design element. "Das Muster besteht aus vielen kleinen Quadraten." (The pattern consists of many small squares.)

Compared to Rechteck (rectangle), Quadrat refers to the more specific shape with four equal sides. Viereck (quadrilateral) is the more general term for any four-sided figure.

🧠 Mnemonics for "das Quadrat"

Article Mnemonic (das)

Think of DAShboard instruments - sometimes they are square and functional, quite *neuter* (neutral) in feeling, like das Quadrat. Or: *'DAS it look square?'* helps remember the neuter article.

Meaning Mnemonic (Shape & Number)

A Quadrat has four corners, neat and true,
And a number times itself, that's its value too! (Think 'quad' for four sides).

🔄 Synonyms & Antonyms for Quadrat

Similar but different terms

• Würfel / Kubus (cube): The three-dimensional equivalent of the *Quadrat*. A *Würfel* has six square faces.
• Quadratwurzel (square root): The number that, when multiplied by itself, gives the original square (e.g., the *Quadratwurzel* of 25 is 5).

😂 A Little Joke

German: Warum ging das Quadrat zum Psychologen?
Weil es zu viele Ecken und Kanten hatte und sich nicht mehr rund fühlte!

English Translation: Why did the square go to the psychologist?
Because it had too many corners and edges (idiomatically: flaws/difficulties) and didn't feel well-rounded anymore!

📜 A Poem about the Quadrat

German:
Vier Seiten, gleich und grad,
Das ist das Quadrat, ganz akkurat.
Vier Winkel, recht und schön,
So kann man es überall seh'n.
Ob Zahl, ob Form, es passt genau,
Klug und nützlich, einfach schlau.

English Translation:
Four sides, equal and straight,
That is the square, quite accurate.
Four angles, right and fine,
So you can see it everywhere shine.
Whether number or shape, it fits just right,
Clever and useful, simply bright.

❓ Little Riddle

German:
Ich habe vier Ecken, alle gleich weit,
Meine Seiten sind gleich lang, zu jeder Zeit.
Bin ich 'ne Zahl, hab ich 'nen Zwilling prompt,
Der mit sich malgenommen auf mich kommt.

Was bin ich?

English Translation:
I have four corners, all equidistant,
My sides are equal length, always consistent.
If I'm a number, I have a twin so grand,
Who multiplied by himself, makes me stand.

What am I?

Solution: Das Quadrat (The Square)

🧩 Other Info about the Quadrat

Word Origin (Etymology)

The word Quadrat comes from the Latin word quadratus, meaning "square" or "squared." This, in turn, derives from quadrum ("square") and quattuor ("four").

Related Terms

• Quadratmeter (m²): *Square meter*, a unit of area measurement.
• Quadratisch: The adjective for *Quadrat* ("a *quadratische* (square) form").
• Quadrieren: The verb for the mathematical operation ("to *quadrieren* (square) a number").
• Quadratur des Kreises: *Squaring the circle*, an idiom for an impossible task.