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Academy11+

11+ Maths · Topic explained

Properties of 2D shapes

Is a square a rectangle? Mathematicians say yes.

The big idea

Flat shapes are named by their sides and angles: how many, which are equal, which are parallel.

Picture it

Like a family: a square is a special rectangle and a special rhombus.

Key words

polygon
A flat shape with straight sides.
parallel
Always the same distance apart, like train tracks.
regular
All sides equal and all angles equal.
quadrilateral
Any shape with 4 straight sides.

Worked examples

  1. 1Warm-up

    Four kinds of triangle

    • Equilateral: 3 equal sides, all angles 60°
    • Isosceles: 2 equal sides; scalene: none equal
    • Right-angled: one angle is 90°
  2. 211+ standard

    I have 4 sides and exactly one pair of parallel sides. What am I?

    • 4 sides: a quadrilateral
    • Exactly one pair of parallel sides: a trapezium
  3. 311+ standard

    A regular octagon: how many sides, and how big is each angle inside?

    • Octagon = 8 sides
    • Angles inside add up to (8 − 2) × 180 = 1080°
    • 1080 ÷ 8 = 135° each
  4. 411+ standard

    What are the properties of a kite?

    • Two pairs of equal sides, next to each other
    • One pair of equal angles
    • Diagonals cross at right angles

The common mistake

The mistake

A square turned on its corner becomes a diamond, so it's not a square any more.

Instead

It's still a square: turning a shape doesn't change its sides or angles.

Why: Four equal sides and four right angles stay the same, whichever way up it is.

Where it comes up in the 11+

'Which shape am I?' clues, sorting shapes, and angles inside polygons.

The video

Video coming soon

We're making a short video that explains properties of 2d shapes step by step. Until then, everything it covers is on this page.

Free printable

Properties of 2D shapes worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Which shape has exactly one pair of parallel sides?

    • Rectangle
    • Trapezium
    • Rhombus
    • Kite
    Show the answer

    Trapezium

    A trapezium has one pair; rectangles and rhombuses have two; a kite has none.

  2. 2. How many sides does a hexagon have?

    • 5
    • 6
    • 7
    • 8
    Show the answer

    6

    Hex means six.

  3. 3. Which triangle has no equal sides?

    • Equilateral
    • Isosceles
    • Scalene
    • Regular
    Show the answer

    Scalene

    Scalene triangles have three different side lengths.