SPACE ACADEMY · TRY, THINK, PLAY

Class 5: Area, perimeter and angles

Read original figures, distinguish their properties and use the conditions shown in a diagram.

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ExploreArea and composite shapes

A step-shaped plot is built from a 7 by 5 unit rectangle with a 1 by 2 unit corner removed, as shown. What is its area in square units?

  1. 2
  2. 33
  3. 35
  4. 18
Need a hint?

Find the area of the whole rectangle, then subtract the area of the missing corner.

Answer & method
Answer B: 33

The whole rectangle is 7 x 5 = 35 square units; the missing corner is 1 x 2 = 2, so the shape covers 35 - 2 = 33 square units.

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ReasonArea and composite shapes

A rectangular plot is 3 times as long as it is wide. Its perimeter is 80 m. What is its area?

  1. 390 sq m
  2. 300 sq m
  3. 330 sq m
  4. 800 sq m
Need a hint?

Half the perimeter is length plus width. Split it using the ratio of length to width.

Answer & method
Answer B: 300 sq m

Length + width = 40 m, made of 4 equal parts. Width = 10 m, length = 30 m. Area = 300 sq m.

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StretchAngles

Three angles sit on a straight line. Two of them measure 44° and 26°. What is the third angle?

44°26°?
  1. 110°
  2. 136°
  3. 70°
  4. 130°
Need a hint?

Angles on a straight line always add up to 180 degrees, even when there are three of them.

Answer & method
Answer A: 110°

180° - 44° - 26° = 110°.

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For grown-ups

Ideas to practise

  • Area and composite shapes. Find the area of the whole and subtract missing parts. Boundary lengths and square units answer different questions.
  • Perimeter. Add the lengths around the outside. Do not confuse perimeter with area.
  • Angles. A right angle is 90 degrees; a straight angle is 180 degrees.
  • Solids and nets. Follow which faces meet when folded. A face touching another in the net cannot be opposite it.
  • Measurement and conversions. Use the same unit before adding or comparing measurements.
  • Reflection and symmetry. A mirror reverses left and right, but not top and bottom.
  • Shapes and their properties. Count straight sides and corners carefully. A curved edge is not a straight side.

A game mission has 8 untimed questions. Only the game saves choices and hints. A finished mission earns one launch charge and participation towards the Command spine in Galaxy Command. The chapter goal is 8 different questions in finished sets; hints and wrong answers count as participation, not mastery. Some craft systems link more than one chapter.

Choose a level

Explore

Foundations: read a representation and practise the underlying idea.

  • Find the area of a composite grid figure
  • Find a missing side or the perimeter of a figure
  • Find an unknown angle using angle facts
  • Find a matching or opposite face on a cube net
  • Judge three statements about shapes and units
Play Explore

Reason

Paper-style reasoning: connect clues, interpret a diagram or work backwards.

  • Find the area of a composite grid figure
  • Find a missing side or the perimeter of a figure
  • Find an unknown angle using angle facts
  • Complete or count a figure using symmetry
  • Count every rectangle hidden in a grid
  • Judge three statements about shapes and units
  • Find the area from rounds or a length ratio
Play Reason

Stretch

Higher-order practice: link conditions, test statements and avoid a tempting wrong method.

  • Find the area of a composite grid figure
  • Find an unknown angle using angle facts
  • Complete or count a figure using symmetry
  • Count every rectangle hidden in a grid
  • Find a matching or opposite face on a cube net
  • Judge three statements about shapes and units
  • Find the area from rounds or a length ratio
Play Stretch

Levels change representations, clues and conditions, not just the numbers. These are practice formats, not validated exam-equivalent difficulty.

Using the feedback

Learning reports distinguish hinted answers from independent first choices. They consider up to 20 recent different, unhinted questions per skill and level, and wait for at least five before suggesting extra practice. Repeating the same question does not add evidence. Reports are practice evidence, not IQ scores, diagnoses, ranks or predictions of competition results.

Ask the learner to explain a drawing or check with objects too. Choose Explore or an earlier chapter when a step feels too large.

Sources & limits

The grade topics use SOF IMO Class 5 published topic syllabus as their primary reference. The SOF sample and CREST previous-year paper below informed representations and reasoning demands. Providers have different topic boundaries; their syllabi are not interchangeable.

Questions, diagrams, picture choices, hints and explanations are original Otterly work, not copied paper questions or publisher artwork. No Olympiad provider is affiliated with or endorses Space Academy. This is not complete exam preparation; follow classroom teaching and check the current official syllabus too. Independent educator review is still needed for difficulty and breadth.

Content and coverage notes. To report a confusing question, describe the grade, chapter, level and question on the contact page. Do not send children’s personal information.

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Original Otterly practice, not an official exam. Game progress stays on this browser.