Mini-Lesson

Geometry and measures

This mini-lesson walks you through the KS3 Geometry & measures strand: perimeter, area & volume, angle facts, properties of shapes and 3-D solids, transformations, and an introduction to Pythagoras.

Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Press Start when you're ready.

Perimeter, area & volume

Perimeter is the distance around

The perimeter is the total distance around the edge of a 2-D shape — add up all the sides. It is a length, so its units are cm, m, km.

Perimeter = 8 + 5 + 8 + 5 = 26 cm. Go all the way around the edge.

Watch out: perimeter (around the edge) is not the same as area (the space inside). We meet area next — keep the two apart.

Area of a rectangle

Area is the space inside

The area is how much flat space a shape covers. It is measured in square units (cm², m²). For a rectangle:

Area = length × widtharea (cm²) = length (cm) × width (cm)

Area = 8 × 5 = 40 cm² — count the little squares: 8 across, 5 down.

Worked example

A rug is 6 m long and 3 m wide.

Area = 6 × 3 = 18 m²

Quick check

Which is which?

?A gardener wants to buy fencing to go all the way round a rectangular lawn. Which measurement does she need?

Calculate

Your turn — area of a rectangle

1A rectangular whiteboard is 9 cm wide and 4 cm tall (a tiny model). Calculate its area.

cm²

Hint: Area = length × width = 9 × 4.

Area of a triangle

A triangle is half a rectangle

A triangle fits inside a rectangle of the same base and height, filling exactly half of it:

Area = ½ × base × heightarea (cm²) = ½ × base (cm) × perpendicular height (cm)

Height must be perpendicular (at a right angle) to the base. Area = ½ × 10 × 6 = 30 cm².

Watch out: the height is the straight-up distance from the base to the tip — not a slanted side.

Calculate

Your turn — area of a triangle

2A triangle has a base of 12 cm and a perpendicular height of 5 cm. Calculate its area.

cm²

Hint: Area = ½ × base × height = ½ × 12 × 5.

Volume of a cuboid

Volume is the space inside a solid

A 3-D solid has volume — how much space it fills, measured in cubic units (cm³, m³). For a cuboid:

Volume = length × width × heightvolume (cm³) = length × width × height

Volume = 5 × 4 × 3 = 60 cm³. Cube up the units: cm³.

Worked example

A box is 10 cm × 2 cm × 3 cm.

Volume = 10 × 2 × 3 = 60 cm³

Calculate

Your turn — volume of a cuboid

3A cuboid measures 4 cm by 3 cm by 2 cm. Calculate its volume.

cm³

Hint: Volume = 4 × 3 × 2.

Match it

Shape ↔ area formula

Tap a shape on the left, then tap its area formula on the right.

Angle facts

Angles on a straight line = 180°

Angles that sit together on a straight line always add up to 180° (a half turn):

Missing angle = 180 − 130 = 50°.

Angles around a point add up to 360° (a full turn) — a whole circle.

Angle facts

Angles around a point = 360°

Go all the way round a single point and the angles total 360°:

Missing angle = 360 − 120 − 150 = 90°.

Vertically opposite angles (across an X where two lines cross) are always equal.

Angle sums

Angles in a triangle = 180°

The three interior angles of any triangle always add up to 180°:

Missing angle = 180 − 70 − 60 = 50°.

Common mistake: some students think the angles add to 360°. In a triangle they always sum to 180°; angles in a quadrilateral sum to 360°.

Calculate

Your turn — missing angle

4Two angles of a triangle are 45° and 85°. Calculate the third angle.

°

Hint: angles in a triangle add to 180. So 180 − 45 − 85.

Sort it

Which angle fact?

Tap the angle fact you would use in each situation.

Angle sums of polygons

Interior angles of a polygon

Split any polygon into triangles from one corner. Each triangle gives 180°, so:

Sum = (n − 2) × 180°n = number of sides

A pentagon (n = 5): (5 − 2) × 180 = 3 × 180 = 540°.

Worked example

A hexagon has 6 sides.

Sum = (6 − 2) × 180 = 4 × 180 = 720°

Quick check

Angle sum of a quadrilateral

?What do the four interior angles of any quadrilateral add up to?

Properties of shapes & 3-D solids

Naming and describing shapes

You should recognise 2-D shapes by their properties, and describe 3-D solids by faces, edges and vertices (corners):

Equilateral triangle — 3 equal sides, 3 angles of 60°.
Square — 4 equal sides, 4 right angles.
Parallelogram — opposite sides parallel and equal.
Cube — 6 faces, 12 edges, 8 vertices.

Congruent shapes are exactly the same size and shape. Similar shapes are the same shape but scaled bigger or smaller — angles stay equal, sides are in the same ratio.

Transformations

Reflection flips a shape over

A reflection flips a shape across a mirror line. Every point moves to the same distance on the other side:

Shape A reflected in the mirror line gives image A' — same size, flipped over.

Transformations

Rotation turns a shape

A rotation turns a shape about a fixed point (the centre of rotation) through an angle, clockwise or anticlockwise:

The blue flag rotated 90° clockwise about the centre becomes the orange flag.

Translation slides a shape (no turning or flipping); enlargement scales it by a scale factor.

Quick check

Name the transformation

?A shape is slid 4 squares right and 2 squares up, without turning or flipping. Which transformation is this?

Pythagoras (intro)

Pythagoras' theorem

In a right-angled triangle, the longest side (the hypotenuse) is opposite the right angle. The theorem links the three sides:

a² + b² = c²c is the hypotenuse (the side opposite the right angle)

c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5. The hypotenuse is always opposite the right angle.

Common mistake: the hypotenuse is the longest side and sits opposite the right angle — never one of the two sides that form the right angle.

Calculate

Your turn — Pythagoras

5A right-angled triangle has the two shorter sides 6 cm and 8 cm. Calculate the length of the hypotenuse.

cm

Hint: c² = 6² + 8² = 36 + 64 = 100, then c = √100.

Quick check

Spot the hypotenuse

?In a right-angled triangle, where is the hypotenuse?

Recap

The facts to know

Perimeter: add up all the sides (a length)

Area of rectangle: length × width

Area of triangle: ½ × base × height

Volume of cuboid: length × width × height

Angles: on a line = 180°, around a point = 360°, in a triangle = 180°

Polygon angle sum: (n − 2) × 180°

Pythagoras: a² + b² = c² (c opposite the right angle)

You've covered the KS3 Geometry & measures strand — measuring shapes, angle facts, transformations and Pythagoras. Press Finish to see your score.

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