Geometry

Properties of 2D & 3D Shapes

Year 3 · Year 4 · Year 5 · Year 6

✓By the end of this lesson students will be able to identify and describe the properties of common quadrilaterals.
✓By the end of this lesson students will be able to identify and name the radius, diameter, and circumference of a circle.
✓By the end of this lesson students will be able to recognise and draw nets of simple 3D shapes.
✓By the end of this lesson students will be able to compare and classify 2D and 3D shapes based on their properties.

Key concepts

Quadrilaterals

A quadrilateral is a 2D shape that has exactly four straight sides and four vertices (corners). The sum of the interior angles of any quadrilateral is 360 degrees. Common quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapeziums, and kites.

Circles

A circle is a 2D shape where all points on its boundary are the same distance from a central point. Key parts of a circle are:

Radius

The radius of a circle is the distance from the centre of the circle to any point on its circumference.

Diameter

The diameter of a circle is a straight line segment that passes through the centre of the circle and has its endpoints on the circumference. It is the longest distance across a circle.

Diameter = 2 × Radius

Circumference

The circumference of a circle is the total distance around the outside edge of the circle.

Nets of 3D Shapes

A net is a 2D (flat) shape that can be folded along its edges to form a 3D (solid) shape. Every 3D shape has at least one net, and many have several different nets. For example, a cube has 11 different nets.

Key facts to remember

1A quadrilateral is any 2D shape with four straight sides and four vertices.
2A square has four equal sides and four right angles.
3A rectangle has opposite sides equal and four right angles.
4The radius of a circle is the distance from the centre to the edge.
5The diameter of a circle is a straight line across the centre, from one edge to the other.
6The diameter is always twice the length of the radius (Diameter = 2 × Radius).
7The circumference is the distance around the outside of a circle.
8A net is a 2D shape that can be folded to make a 3D shape.

Worked examples

Example 1

Describe the properties of a square and a rectangle, highlighting their similarities and differences.

IA square has four equal straight sides.

IIA square has four right angles (90 degrees).

IIIA square has four vertices.

IVA rectangle has four straight sides, with opposite sides being equal in length.

VA rectangle has four right angles (90 degrees).

VIA rectangle has four vertices.

VIISimilarity: Both have four sides, four vertices, and four right angles.

VIIIDifference: All four sides of a square are equal, whereas only opposite sides of a rectangle are equal (unless it is also a square).

Answer

A square has four equal sides, four right angles, and four vertices. A rectangle has four sides with opposite sides equal, four right angles, and four vertices. Both have four sides, four vertices, and four right angles, but a square has all sides equal, while a rectangle only has opposite sides equal.

Remember that all squares are rectangles, but not all rectangles are squares!

Example 2

A circular clock face has a radius of 15 cm. What is its diameter?

IIdentify the given information: The radius (r) is 15 cm.

IIRecall the relationship between radius and diameter: Diameter = 2 × Radius.

IIISubstitute the given radius into the formula: Diameter = 2 × 15 cm.

IVCalculate the result: Diameter = 30 cm.

Answer

The diameter of the clock face is 30 cm.

The diameter is always twice the length of the radius.

Example 3

Imagine a 3D shape with 6 square faces. Which 3D shape is this, and what would its net look like?

IIdentify the 3D shape: A shape with 6 square faces is a cube.

IIVisualise the faces: A cube has 6 identical square faces.

IIIConsider how these faces can be laid out flat: A common net for a cube looks like a 'T' shape, with four squares in a row and one square above and one square below the second square in the row.

IVDescribe the net: The net consists of 6 squares arranged so they can fold up to form the cube without overlapping or leaving gaps.

Answer

The 3D shape is a cube. A common net for a cube is made of 6 squares, often arranged in a cross or 'T' shape, where four squares are in a line and one square is attached to the top of the second square in the line, and another square is attached to the bottom of the second square in the line.

There are 11 different nets that can form a cube.

Common mistakes

✗Confusing the properties of a rhombus with a square (a rhombus has equal sides but not necessarily right angles).
✗Mixing up the radius and diameter, or forgetting that the diameter is twice the radius.
✗Drawing nets that overlap when folded, or nets that have gaps and won't form a closed 3D shape.
✗Incorrectly counting the number of faces, edges, or vertices of 3D shapes.

Exam tips

★Always draw diagrams or sketch the shapes to help you visualise their properties.
★When describing shapes, use precise mathematical vocabulary like 'parallel', 'perpendicular', 'right angle', 'equal length'.
★For nets, imagine folding the 2D shape in your mind to check if it forms the correct 3D shape.
★Practise identifying and drawing nets for common 3D shapes like cubes, cuboids, and triangular prisms.

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