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NSW SelectiveYear 7 entry

2D shapes and angles for the Selective maths test

Independent. Not affiliated with the NSW Department of Education.

2D shape questions in the Selective maths test rest on a few fixed rules: angle totals, shape properties, perimeter and area. Your child labels the diagram, picks the rule that links what's given to what's asked, then checks.

Watch the full lessonPlay the preview

The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

2D Shapes & Geometry (lesson preview)

A short preview from the SelectiveReady lesson “2D Shapes & Geometry”, on perimeter versus area and the half in a triangle's area, for the NSW Selective test.

Published:

Read the video transcript

This is maybe the most common trap in all of geometry. Mixing up perimeter and area. Just remember it like this. Perimeter is like the fence that goes around a yard. You add up all the side lengths. Area is the grass inside the yard. That's when you have to use a formula, like length times width. Perimeter is around, area is inside. Got it? And speaking of area, here is trap number one, the absolute classic. The formula for a triangle's area seems easy, right? But there's this one tiny little piece that so many people forget when the pressure's on. It's not just base times height. No, it's one half times base times height. If you forget that little one half part, your answer will be double what it should be, which is exactly the mistake the exam is hoping you'll make. So please burn that one half into your brain for any triangle area question.

2D Shapes & Geometry is a full lesson in the SelectiveReady app. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published. The preview plays here with English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns that every shape has a personality: the traits that never change, however the shape is drawn. They'll be able to use the four angle rules, tell shapes apart by their properties, keep perimeter and area separate and find a triangle's area without the classic slip.

The clip covers the two biggest traps: mixing up perimeter and area, and forgetting the half in a triangle's area. The full lesson adds the angle toolkit, a worked angle question and a cheat sheet.

3

How do shapes and angles show up in the Selective maths test?

Shape questions sit inside the Mathematical Reasoning section, usually with a diagram. The Department doesn't say how many there will be: questions come from a range of maths content areas2NSW Education · 13 October 2026 · Published.

PartThe Department's rule
Questions and time352NSW Education · 12 October 2026 · Published questions in 402NSW Education · 12 October 2026 · Published minutes
Options per question52NSW Education · 12 October 2026 · Published
ToolsNo calculator2NSW Education · 12 October 2026 · Published; 23NSW Education · 12 October 2026 · Published sheets of working paper, more on request
Maths neededconcepts from the NSW curriculum up to Year 62NSW Education · 12 October 2026 · Published

Working paper matters here. A quick sketch with every length and angle labelled turns a busy diagram into a few clear facts.

4

What are the angle rules?

The lesson's four rules solve most angle questions, and the triangle rule is the one to remember above all. The last row follows from it, because a four-sided shape splits into two triangles.

Four angle rules: a right angle is 90°, a straight line 180°, a triangle's angles 180°, and angles around a point 360°.
RuleThe totalHow to spot it
A right angle90°A small square drawn in the corner
Angles on a straight lineAdd to 180°Angles side by side along one line
Angles in a triangleAdd to 180°Any triangle, tall, thin or tilted
Angles around a pointAdd to 360°Angles meeting at one spot, like a wheel
Angles in a four-sided shapeAdd to 360°Squares, rectangles and other quadrilaterals
5

What is the difference between perimeter and area?

Perimeter is the fence around a yard: add up every side. Area is the grass inside: for a rectangle, multiply length by width. The lesson's line is easy to remember: perimeter is around, area is inside.

ShapePerimeterArea
RectangleAdd all four sidesLength × width
SquareFour times one sideSide × side
TriangleAdd all three sides½ × base × height
A 6 cm by 4 cm rectangle20 cm24 cm²

Perimeter is a length, so it's in cm or m. Area is in square units, such as cm² or m².

6

What is the method for shape questions?

Sketch, label, pick the rule, then check. The checking step is what the lesson calls the habit that separates good answers from great ones.

  1. Sketch and label

    Copy the shape onto working paper. Write every length and angle the question gives, and mark right angles.

  2. Name what's asked

    An angle, a perimeter or an area? Note it on working paper, because the answer's units depend on it.

  3. Choose the rule

    Pick the rule that joins a known fact to the unknown. Missing sides often come from the opposite side of the shape.

  4. Check it adds up

    Add the angles back to 180° or 360°, or rebuild the perimeter side by side.

7

What does a worked angle example look like?

We wrote this question to show two rules working together.

Our practice question
Triangle ABC sits on a straight line, which carries on past corner C. Inside the triangle, angle B is 55°. Outside the triangle at C, the angle on the straight line is 130°. How big is angle A?
StepWhat your child does
Sketch and labelDraw the triangle, mark 55° at B and 130° outside at C
First rule: straight lineThe inside angle at C is 180° − 130° = 50°
Second rule: triangleAngle A is 180° − 55° − 50° = 75°
Check75° + 55° + 50° = 180°, so the angles fit

The traps: 50° is angle C, one step short, and 125° forgets angle C altogether.

8

Which mistakes catch most children?

The most common trap in geometry is mixing up perimeter and area. In a triangle, forgetting the half is the classic slip, and it doubles the answer.

TrapWhat it looks likeThe fix
Perimeter or areaMultiplying when the question asks for the fence aroundAround means add, inside means multiply
The missing halfA triangle with base 8 cm and height 5 cm given as 40 cm²½ × 8 × 5 = 20 cm²
A tilted shapeCalling a square turned on its corner a diamondCheck the sides and angles, not the direction
Trusting the pictureMeasuring a diagram that isn't drawn to scaleUse the numbers given, not the look
9

Can my child try one on their own?

Here is a perimeter question from our free maths set. Your child answers it, then checks the steps below.

Practice question · SEL-MA-TST-20

Georgia's garden bed is U-shaped. All its corners are right angles. Some of the side lengths are shown.

Georgia puts edging all the way around the outside of the garden bed. How many metres of edging does she need?

  1. A

    33 m

  2. B

    40 m

  3. C

    45 m

  4. D

    50 m

  5. E

    76 m

Show answer and explanation

Answer: D

Answer: D (50 m)

  1. The right side matches the left side: 8 m.
  2. The top of the right arm is 12 − 4 − 4 = 4 m.
  3. The two inner sides of the gap are the same length: 5 m each.
  4. Add all 8 sides: 12 + 8 + 4 + 5 + 4 + 5 + 4 + 8 = 50 m.

Why the other options are wrong

  • A (33 m): This adds only the five labelled sides and misses the three unlabelled ones.
  • B (40 m): This is the perimeter of a full 12 m by 8 m rectangle, which leaves out the two 5 m sides inside the gap.
  • C (45 m): This misses one of the two 5 m sides inside the gap.
  • E (76 m): This is the area of the garden bed in square metres (96 − 20), not the distance around it.

  1. Find the missing sides

    The right side matches the left side: 8 m. The top of the right arm is 12 − 4 − 4 = 4 m.

  2. Spot the hidden pair

    The two inner sides of the gap are the same length: 5 m each.

  3. Add all eight sides

    12 + 8 + 4 + 5 + 4 + 5 + 4 + 8 = 50 m, so the answer is D. Option E, 76, is the area in square metres.

10

Which geometry skills should my child practise?

The angle rules, perimeter of shapes with steps or gaps, and area of rectangles and triangles. Practise a few at a time, always with a sketch.

Missing angles

Draw triangles and straight lines with one angle hidden. Your child names the rule before working it out.

Measure at home

Find the perimeter and area of a room, a garden bed or a table, in metres or centimetres.

Shapes with gaps

Draw L and U shapes on grid paper. Find the missing sides first, then count the perimeter.

11

Questions parents ask about 2D shapes for Selective

Does my child need a protractor?

Not in the test room. Some practice questions, including one in our free set, show a protractor on screen to read, so practise reading both scales at home.

Are the diagrams drawn to scale?

Don't rely on it. Use the lengths and angles written on the diagram, not how big things look.

What's the difference between a square and a rhombus?

Both have four equal sides. A square also has four right angles.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Mathematical Reasoning →Lesson: 3D Shapes & Space →Lesson: Measurement & Unit Conversions →Lesson: Algebraic Thinking →Free Selective practice test →

Sources and checks

  1. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  2. Selective high school practice tests

    NSW Department of Education · Checked 12 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.

  3. Placement test

    NSW Department of Education · Checked 12 October 2026 · CC BY 4.0 (NSW Department of Education copyright notice); quotes credited

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