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.

Make a guess: same length of fence, so same amount of grass?

Mission 1Same length of fence. Same amount of grass?
Mission 2Do a giant triangle's angles add up to more?
Mission 3How long is the shortcut across the corner?

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.

Mission 1 check

Same length of fence. Same amount of grass?

?Two goat pens each use 20 m of fence. Pen A is 6 m by 4 m. Pen B is 9 m by 1 m. Which pen has more space inside?

Match it

Shape ↔ area formula

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

Mission 2 of 3

Do a giant triangle's angles add up to more?

Make a guess: do a giant triangle's angles add up to more?

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?

Mission 2 check

Do a giant triangle's angles add up to more?

?One triangle is drawn on a phone screen. Another is marked out with rope on a school field. What can you say about the angles inside each one?

Mission 3 of 3

How long is the shortcut across the corner?

Make a guess: is the shortcut across the corner 7 m too?

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?

Mission 3 check

How long is the shortcut across the corner?

?You walk 5 m along one edge of a field. You turn through a right angle and walk 12 m. How far are you from your start, in a straight line?

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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