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Year 7 · Key Stage 3 · free KS3 maths worksheet

Properties of 2D and 3D shapes

12 original questions, 31 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Write down the mathematical name of a polygon with exactly five sides.

1 mark
Show answer
pentagon
2

The diagram shows a circle with centre O.

  1. Write down the mathematical name of each of the lines a, b and c.
  2. What is the name for the distance all the way round a circle?
  3. The radius of this circle is 3 cm. Write down the length of the diameter.
OacbDiagram NOT accurately drawn
4 marks
Show answer
a) a = radius, b = diameter, c = chord b) circumference c) 6 cm
3

The diagram shows the quadrilateral ABCD.

  1. Write down the side that is parallel to AB.
  2. Write down a side that is perpendicular to AB.
  3. Write down the mathematical name of quadrilateral ABCD.
ABCDDiagram NOT accurately drawn
3 marks
Show answer
a) DC b) AD c) trapezium
4
  1. A quadrilateral has exactly one pair of parallel sides. Write down the mathematical name of this quadrilateral.
  2. A different quadrilateral has two pairs of parallel sides. All four of its sides are equal in length but none of its angles are right angles. Write down the mathematical name of this quadrilateral.
2 marks
Show answer
a) trapezium b) rhombus
5

Write down the mathematical name of each triangle.

  1. All three sides are the same length.
  2. None of the sides are the same length and none of the angles are the same size.
  3. Two sides are the same length and one angle is 90°.
3 marks
Show answer
a) equilateral b) scalene c) right-angled isosceles
6
  1. Write down the order of rotational symmetry of a regular hexagon.
  2. Write down the number of lines of symmetry of a regular hexagon.
2 marks
Show answer
a) 6 b) 6
7

Here is a triangular prism.

  1. Write down the number of faces of a triangular prism.
  2. Write down the number of edges of a triangular prism.
2 marks
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a) 5 b) 9
8

The diagram shows five quadrilaterals, labelled A, B, C, D and E, drawn on a centimetre grid.

  1. Write down the letters of the pair of congruent quadrilaterals.
  2. Write down the mathematical name of quadrilateral A.
ABCDE
2 marks
Show answer
a) A and C b) parallelogram
9

The diagram shows four rectangles, A, B, C and D, drawn on a centimetre grid.

  1. Which rectangle is mathematically similar to rectangle A?
  2. Explain why rectangle D is not similar to rectangle A.
ABCD
3 marks
Show answer
a) B b) The sides of D are not the sides of A multiplied by the same number
10

On the left of the isometric grid is a cuboid made from centimetre cubes.

  1. Write down the length, width and height of the cuboid.
  2. How many centimetre cubes make the cuboid?
  3. On the right of the grid, draw a cuboid 2 cm long, 2 cm wide and 1 cm high.
3 marks
Show answer
a) 3 cm by 2 cm by 2 cm b) 12 c) A 2 by 2 by 1 cuboid drawn along the grid lines
11

The diagram shows a net. The faces are labelled A to F.

  1. Write down the name of the 3D solid the net folds to make.
  2. When the net is folded, which face is opposite face A?
  3. Which face is opposite face C?
ABCDEFDiagram NOT accurately drawn
3 marks
Show answer
a) cube b) F c) E
12

The diagram shows the net of a 3D solid. It is made from three rectangles and two equilateral triangles.

  1. Write down the name of the solid.
  2. Write down the number of edges the solid has.
  3. Ravi says, "The solid has 6 faces." Is Ravi correct? Give a reason.
Diagram NOT accurately drawn
3 marks
Show answer
a) triangular prism b) 9 c) No, it has 5 faces (3 rectangles and 2 triangles)

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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