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Mathematics
Numbers, Shapes & Proofs
The constants, shapes and terms worth actually knowing.
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What is the value of pi to two decimal places?
Shapes, Angles and Space
The part of maths you can see. Ten questions on shapes and the space they take up.
About this topic
Geometry is the oldest branch of mathematics still taught in more or less its original form, and the one that survives longest in everyday life. Anyone laying a floor, hanging a picture or working out whether a sofa will fit through a door is doing it, whether or not they would call it that. These questions cover the naming of shapes, the behaviour of angles, and the difference between measuring an edge, a surface and a volume — the distinction people most often get wrong when a job involves buying materials.
Questions & answers
Shapes, Angles and Space: all 10 questions and answers
Every question in this quiz is listed below with its correct answer and the reasoning behind it. Play first if you would rather not see the answers — or read through as a study sheet.
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1How many sides does a pentagon have?
- A Six
- B Seven
- C Four
- D Five Correct
Answer: D. Five
Why: From the Greek "pente". A hexagon has six and an octagon eight.
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2The angles inside a quadrilateral add up to how many degrees?
- A 270
- B 540
- C 360 Correct
- D 180
Answer: C. 360
Why: Any four-sided shape totals 360, because it can be split into two triangles of 180 each.
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3What is the area of a rectangle 6m long and 4m wide?
- A 48 square metres
- B 24 square metres Correct
- C 20 square metres
- D 10 square metres
Answer: B. 24 square metres
Why: Area multiplies the two dimensions. Its perimeter would be 20 metres, which is a different measurement entirely.
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4A triangle with all three sides equal is called what?
- A Equilateral Correct
- B Isosceles
- C Scalene
- D Obtuse
Answer: A. Equilateral
Why: Its angles are all 60 degrees. Isosceles has two equal sides, scalene none.
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5An angle greater than 90 but less than 180 degrees is called what?
- A Acute
- B Reflex
- C Right
- D Obtuse Correct
Answer: D. Obtuse
Why: Acute is under 90 and reflex is over 180.
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6How many faces does a cube have?
- A Twelve
- B Four
- C Six Correct
- D Eight
Answer: C. Six
Why: It also has eight vertices and twelve edges. All six faces are identical squares.
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7The volume of a box measuring 2m by 3m by 4m is what?
- A 48 cubic metres
- B 24 cubic metres Correct
- C 9 cubic metres
- D 12 cubic metres
Answer: B. 24 cubic metres
Why: Volume multiplies all three dimensions, which is why it is measured in cubic units.
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8A line that touches a circle at exactly one point is called what?
- A A tangent Correct
- B A radius
- C A chord
- D A diameter
Answer: A. A tangent
Why: A chord crosses the circle at two points; the diameter is the longest chord.
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9The diameter of a circle is what, compared with its radius?
- A Half as long
- B The same
- C Pi times as long
- D Twice as long Correct
Answer: D. Twice as long
Why: The circumference is pi times the diameter, which is where the constant enters.
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10Two shapes that are the same shape but different sizes are described as what?
- A Parallel
- B Symmetrical
- C Similar Correct
- D Congruent
Answer: C. Similar
Why: Congruent means identical in both shape and size. Similar shapes share angles but not dimensions.
Frequently asked questions about Shapes, Angles and Space
How many questions are in Shapes, Angles and Space?
Shapes, Angles and Space has 10 questions and takes about 6 minutes to finish. It is rated Easy and sits in our Mathematics category.
How is Shapes, Angles and Space scored?
Each of the 10 correct answers adds 10 XP, up to 100 XP for a clean run. Wrong answers cost you nothing, and your full question-by-question review is shown at the end.
Are the answers to Shapes, Angles and Space explained?
Yes. All 10 questions carry a written explanation of why the correct answer is right, so the quiz works as a study sheet as well as a test.
Can I replay Shapes, Angles and Space?
Yes, as often as you like. The questions and the answer options are reshuffled on each run, and you can use Practice Mistakes afterwards to retry only the ones you missed. No account is needed to play.
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