Volume of a Prism: Triangular, Pentagonal + Examples
Math Education6 min read
Math Education
7 min read
Properties of Quadrilaterals: The Complete Table
Published: 12.08.2026·Updated: 12.08.2026
Dewi Lestari
Mathematics Specialist
A quadrilateral is a plane shape bounded by four sides with four angles. Six types are studied at school, each distinguished by its side, angle and diagonal properties. The topic is taught in Year 7 after plane shapes in primary school.
The One Property Every Quadrilateral Shares
Whatever the type, the four angles always total 360°. This rule appears in almost every question, and its origin is simple: any quadrilateral splits into two triangles, each totalling 180°.
The Complete Properties Table
| Shape | Sides | Angles | Diagonals |
|---|---|---|---|
| Square | All four equal | All four 90° | Equal, perpendicular, bisect each other |
| Rectangle | Opposite sides equal | All four 90° | Equal, bisect each other |
| Parallelogram | Opposite sides equal and parallel | Opposite angles equal | Bisect each other, not equal |
| Rhombus | All four equal | Opposite angles equal | Perpendicular, bisect each other |
| Kite | Two pairs of adjacent sides equal | One pair of opposite angles equal | Perpendicular, one bisects the other |
| Trapezium | One pair of parallel sides | Co-interior angles total 180° | No special property |
The Family Tree of Quadrilaterals
This part is rarely taught and explains almost every confusion in the topic. Quadrilaterals are not six separate boxes but a nested family:
- A square is a rectangle with all four sides equal
- A square is also a rhombus with all four angles at 90°
- Rectangles and rhombuses are both parallelograms
- A parallelogram is a trapezium with two pairs of parallel sides
So when a question asks "is a square a rectangle?", the answer is yes. The square is the most specialised shape, carrying every property of its relatives above it.
Perimeter and Area Formulas
| Shape | Perimeter | Area |
|---|---|---|
| Square | 4s | s × s |
| Rectangle | 2(l + w) | l × w |
| Parallelogram | 2(a + b) | base × height |
| Rhombus | 4s | ½ × d₁ × d₂ |
| Kite | 2(a + b) | ½ × d₁ × d₂ |
| Trapezium | sum of all sides | ½ × (a + b) × h |
Note that the rhombus and the kite share the same area formula, half the product of the diagonals. The reason is the same for both: their diagonals are perpendicular. See also area of a parallelogram and trapezium.
The Mistakes That Actually Cost Marks
1. Thinking a square is not a rectangle. The number one cause in true-or-false questions. A square meets every condition of a rectangle.
2. Using the slanted side as a parallelogram's height. The height must be perpendicular to the base, not the length of the slanted side.
3. Using sides instead of diagonals for a rhombus. Its area formula uses both diagonals, not the side length.
4. Thinking a parallelogram has lines of symmetry. It has none — see lines and order of symmetry.
5. Forgetting the angle sum is 360°, not 180°. The 180° belongs to triangles.
