Types of Quadrilaterals

What is a quadrilateral?

A quadrilateral is a flat (2D) shape with four straight sides and four corners. The word looks tricky, but it just joins two Latin words: quad meaning "four" and lateral meaning "side". So a quadrilateral is simply a four-sided shape.

Quadrilaterals are all around you: the page of a book, a window, a door, a phone screen, a football pitch and a kite flying in the sky are all quadrilaterals. They belong to the bigger family of shapes called polygons (shapes made of straight sides), which you can explore more in our lesson on 2D and 3D shapes.

One amazing rule is true for every quadrilateral: its four inside angles always add up to 360°. This is because you can always split a quadrilateral into two triangles, and each triangle's angles add up to 180°, so two of them make 360°.

The main types of quadrilaterals

There are six special quadrilaterals you should know.

• Square — four equal sides and four right angles (90°). The most regular and balanced quadrilateral.
• Rectangle — four right angles, but only opposite sides are equal. A square is a special rectangle.
• Parallelogram — two pairs of parallel sides; opposite sides are equal and opposite angles are equal, but the corners are usually not right angles (it looks "leaning").
• Rhombus — four equal sides like a square, but pushed over so the angles are not 90°. Often called a "diamond".
• Trapezium — exactly one pair of parallel sides.
• Kite — two pairs of equal sides that are next to each other (adjacent), like the kite you fly.

How they are related

These shapes form a family tree. A square is the most special of all — it is at the same time a rectangle (it has four right angles), a rhombus (it has four equal sides), and a parallelogram (its opposite sides are parallel). A square is like the "champion" that holds every title at once.

A rectangle and a rhombus are both special parallelograms. A rectangle is a parallelogram that gained right angles; a rhombus is a parallelogram that gained equal sides. If you give a parallelogram both right angles and equal sides, you get a square.

A diagram in words

Imagine six shapes drawn in a row.

A square sits flat and even, like a tile, with little dashes on every side to show they are all equal and small squares in each corner for the right angles.

Next to it, a rectangle is a stretched square — wider than it is tall, with right-angle marks in the corners but only the top and bottom sides matching, and the two longer sides matching.

The parallelogram looks like a rectangle that has been pushed sideways, so it leans like a stack of books sliding over.

The rhombus stands on one of its points like a diamond on a playing card, all four sides equal but tilted.

The trapezium has a long flat bottom and a shorter flat top that are parallel, joined by two slanting sides.

Finally the kite points upward like a real flying kite: two short equal sides at the top meeting two longer equal sides at the bottom.

Worked example 1

A four-sided shape has all sides 6 cm long, and each corner is a right angle. What is it?

All four sides are equal (6 cm) and all four angles are right angles. A shape with both of these is a square.

Worked example 2

A shape has top and bottom sides of 10 cm (parallel to each other) and slanting left and right sides of 4 cm and 7 cm that are not parallel. What is it?

Only one pair of sides is parallel (the top and bottom), and the other two sides are different lengths and not parallel. That makes it a trapezium.

Worked example 3

A quadrilateral has three angles of 100°, 80° and 95°. What is its fourth angle?

The four angles must total 360°. Add the three you know: 100 + 80 + 95 = 275°. Subtract from 360: 360 − 275 = 85°. The missing angle is 85°.

Why this matters

Knowing the types of quadrilaterals helps you describe the world precisely and solve problems quickly. If you know a shape is a rectangle, you instantly know its opposite sides are equal — which is exactly what you need to work out its area and perimeter without measuring every side. Builders use these properties to make sure walls are square (true right angles), and designers use parallelograms and trapeziums to create patterns that tessellate (fit together with no gaps). The "360° rule" also lets you find a missing angle, just as you saw above. To put quadrilaterals to work measuring space, see our lesson on area and perimeter.

Activity: build the quadrilateral family

You need some straws (or strips of card) and a little modelling clay or sticky tack.

1. Cut straws into pieces and use balls of clay as the corners to build each quadrilateral: a square, a rectangle, a parallelogram, a rhombus, a trapezium and a kite.
2. Now do the "push test". Hold a square model and gently push one corner sideways. Watch it slump into a rhombus or parallelogram! This shows why builders add a diagonal brace to triangles, not quadrilaterals.
3. Sort them: make two piles — shapes with at least one pair of parallel sides, and shapes without.
4. Challenge: can you turn your rectangle into a square just by changing the side lengths? Which other shapes can "become" a square, and which cannot? Write down what you discover.