Quadrangle — Definition, Formula & Examples
Quadrangle is simply another name for a quadrilateral, meaning any closed, flat shape that has exactly four sides and four angles. You will see both words used interchangeably in geometry.
A quadrangle is a polygon with four vertices, four edges, and four interior angles whose measures sum to . The term derives from the Latin 'quadri-' (four) and 'angulus' (angle), emphasizing the four-angle property of the figure.
Worked Example
Problem: A quadrangle has interior angles measuring 90°, 85°, and 110°. Find the fourth angle.
Step 1: Use the fact that the interior angles of any quadrangle sum to 360°.
Step 2: Add the three known angles.
Step 3: Solve for the missing angle.
Answer: The fourth angle measures .
Why It Matters
You may encounter "quadrangle" in older textbooks, standardized tests, or architecture (many college campuses have a "quad" — a four-sided courtyard). Recognizing it as a synonym for quadrilateral prevents confusion when switching between sources.
Common Mistakes
Mistake: Thinking a quadrangle is a different shape from a quadrilateral.
Correction: They are the same thing. 'Quadrilateral' stresses four sides (lateral = side), while 'quadrangle' stresses four angles (angle). Both describe any four-sided polygon.