Math · Unit 8

Geometry

Angles, polygons, perimeter, area and transformations

Formal geometry starts by giving precise names to things everyone can already see, and the precision is what allows anything to be proved.

The unit covers angles and angle rules, polygons and their properties, perimeter and area, and transformations - reflection, rotation, translation - which are the operations that leave a shape essentially unchanged.

This unit breaks down into 21 short steps and 120 questions, starting at difficulty 2 and building to 3. Below you can see exactly what it covers, how the path is structured, and worked examples with explanations.

Steps: 21
Questions: 120
Difficulty: 2-3

What this unit covers

Perimeter
Symmetry and Transformations
Area
Angles
Polygons and Their Sides

Where this fits

Follows Shapes and Patterns. Geometry and Trigonometry continues it.

Where people slip

Perimeter and area are independent. Two shapes can have the same perimeter and wildly different areas, which is why the two are so easy to confuse in word problems.

How the unit is structured

Geometry runs as 21 short steps that unlock in order. 15 are practice rounds and 6 are challenge rounds that pull together everything before them. Questions start at difficulty 2 and climb to 3 as you progress.

Step 1 · easierStep 21 · harder

Challenge rounds

Example questions

30 real questions from this unit, with the answer and the reason behind it, grouped by what they practise. There are 120 in the unit altogether.

Angles

Build the sentenceLevel 2
1. Build a true sentence about a right angle.
Answer: A right angle is 90 degrees
A right angle is 90 degrees.
Choose all that applyLevel 2
2. Which of these angle measures are acute?
- 30 degreescorrect
- 75 degreescorrect
- 90 degrees
- 110 degrees
Acute angles are less than 90 degrees, so 30 and 75 degrees qualify.
Fact or fibLevel 2
3. An obtuse angle is bigger than 90 degrees.
Answer: True
An obtuse angle is greater than 90 degrees but less than 180 degrees.
Fill the blankLevel 2
4. The three angles inside a triangle add up to ____ degrees.
- 180correct
- 90
- 360
- 100
The angles in any triangle always add up to 180 degrees.
Match the pairsLevel 2
5. Match each angle type to its measure.
Answer: Right angle = 90 degrees; Straight angle = 180 degrees; Acute angle = Less than 90 degrees
A right angle is 90 degrees, a straight angle is 180 degrees, and an acute angle is less than 90 degrees.
Multiple choiceLevel 2
6. An angle smaller than 90 degrees is called what?
- Acutecorrect
- Obtuse
- Right
- Straight
An angle less than 90 degrees is an acute angle.

Area

Build the sentenceLevel 2
7. Build a true sentence about area.
Answer: Area is the space inside a shape
Area is the space inside a shape.
Fact or fibLevel 2
8. The area of a rectangle 2 cm by 6 cm is 12 square cm.
Answer: True
Area is 2 x 6 = 12 square cm.
Fill the blankLevel 2
9. The amount of flat space inside a shape is its ____.
- areacorrect
- perimeter
- angle
- edge
Area measures the space covered inside a flat shape.
Multiple choiceLevel 2
10. A rectangle is 5 cm long and 3 cm wide. What is its area?
- 15 sq cmcorrect
- 16 sq cm
- 8 sq cm
- 30 sq cm
Area is length x width = 5 x 3 = 15 sq cm.
Choose all that applyLevel 3
11. Which of these correctly give an area?
- Length x width for a rectanglecorrect
- Base x height / 2 for a trianglecorrect
- Side + side for a square
- 2 x (length + width) for a rectangle
Rectangle area is length x width, and triangle area is base x height / 2; the other two describe a perimeter.
Guess the numberLevel 3
12. A rectangle is 12 cm long and 5 cm wide. What is its area, in square cm?
Answer: 60 sq cm
Area is length x width = 12 x 5 = 60 square cm.

Perimeter

Build the sentenceLevel 2
13. Build a true sentence about perimeter.
Answer: Perimeter is the distance around a shape
Perimeter is the distance around a shape.
Fill the blankLevel 2
14. To find the perimeter of a shape you ____ the lengths of all its sides.
- addcorrect
- multiply
- divide
- subtract
Perimeter is found by adding up the lengths of every side.
Choose all that applyLevel 3
15. Which shapes have a perimeter of 20 cm?
- A square with a side of 5 cmcorrect
- A rectangle 6 cm by 4 cmcorrect
- A rectangle 8 cm by 3 cm
- An equilateral triangle with a side of 5 cm
A square with side 5 cm and a rectangle 6 cm by 4 cm both have a perimeter of 20 cm.
Fact or fibLevel 3
16. Perimeter is measured in square units like square cm.
Answer: False
Perimeter is a length, so it uses units like cm; square units measure area.
Guess the numberLevel 3
17. A regular pentagon has sides of 11 cm each. What is its perimeter, in cm?
Answer: 55 cm
A regular pentagon has 5 equal sides, so 5 x 11 = 55 cm.
Match the pairsLevel 3
18. Match each shape to its perimeter formula.
Answer: Square = 4 x side; Rectangle = 2 x (length + width); Equilateral triangle = 3 x side
A square is 4 x side, a rectangle is 2 x (length + width), and an equilateral triangle is 3 x side.

Polygons and Their Sides

Build the sentenceLevel 2
19. Build a true sentence about a triangle.
Answer: A triangle has three sides
A triangle has three sides.
Choose all that applyLevel 2
20. Select the shapes that have exactly 4 sides.
- Squarecorrect
- Rectanglecorrect
- Triangle
- Hexagon
A square and a rectangle each have 4 sides; a triangle has 3 and a hexagon has 6.
Match the pairsLevel 2
21. Match each polygon to its number of sides.
Answer: Heptagon = 7 sides; Octagon = 8 sides; Decagon = 10 sides
A heptagon has 7 sides, an octagon has 8, and a decagon has 10.
Multiple choiceLevel 2
22. How many sides does a hexagon have?
- 6correct
- 5
- 7
- 8
A hexagon has 6 sides, like the shape of a honeycomb cell.
Fill the blankLevel 3
23. A polygon with 10 equal sides is called a ____.
- decagoncorrect
- octagon
- nonagon
- heptagon
A ten-sided polygon is a decagon.
Odd one outLevel 3
24. Which shape does NOT have all sides equal in length?
- Rectanglecorrect
- Square
- Rhombus
- Equilateral triangle
A rectangle has two long and two short sides, while a square, rhombus, and equilateral triangle have all equal sides.

Symmetry and Transformations

Choose all that applyLevel 2
25. Which of these have at least one line of symmetry?
- Squarecorrect
- Rectanglecorrect
- Scalene triangle
- Letter P
A square and a rectangle each have lines of symmetry; a scalene triangle and the letter P have none.
Fact or fibLevel 2
26. A rectangle that is not a square has exactly 2 lines of symmetry.
Answer: True
A non-square rectangle has 2 lines of symmetry, one horizontal and one vertical.
Multiple choiceLevel 2
27. How many lines of symmetry does a square have?
- 4correct
- 2
- 1
- 8
A square has 4 lines of symmetry: two through the middles of the sides and two through the corners.
Build the sentenceLevel 3
28. Build a true sentence about a reflection.
Answer: A reflection makes a mirror image
A reflection makes a mirror image.
Fill the blankLevel 3
29. Flipping a shape over a line to make a mirror image is called a ____.
- reflectioncorrect
- rotation
- translation
- tessellation
A reflection flips a shape across a line to form a mirror image.
Match the pairsLevel 3
30. Match each regular shape to its number of lines of symmetry.
Answer: Equilateral triangle = 3 lines; Square = 4 lines; Regular pentagon = 5 lines
An equilateral triangle has 3 lines, a square has 4, and a regular pentagon has 5.

Where these questions come from. Each unit starts as a plan of the concepts it should cover and the difficulty it should span. Questions are written against that plan with AI assistance, then checked by a validator that rejects anything without a single defensible answer, an explanation, or plausible wrong options. How we write questions sets out the whole process, and corrections are fixed in the bank and reach the site and the app the same day.

How you practise

This unit mixes 14 different question formats, so you are recalling and applying rather than recognising the same layout every time.

Build the sentence
Choose all that apply
Fact or fib
Fill the blank
Guess the number
Match the pairs
Multiple choice
Odd one out
Picture question
Put in order
Sort into groups
Spell it
True or false
Type the answer

Practise Geometry

120 questions across 21 steps. Start with step one and crawl at your own pace.

Play this unit

Read about Geometry

Explainers from our blog on what this unit covers. Each one ends with real questions from the bank.

How to Find the Area of a Trapezoid Step by StepLearn how to find the area of a trapezoid using the two parallel sides and perpendicular height, with a clear formula, example, and common error checks.August 17, 2026 · 5 min read

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