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Shape assembly

Assembly questions show pieces and ask which shape they make when fitted together (or which piece is missing). Pieces can be turned but not flipped unless the question says so, and they must fit without gaps or overlaps.

What is tested

  • Which pieces join to make a given shape
  • Finding the missing piece
  • Using area (counting squares) to check a fit

Worked example

Two identical right-angled triangles are joined along their longest side. The two short sides of each triangle are equal. What shape do they make?

  1. The longest side is the diagonal of the finished shape.
  2. Joining along it puts the two right angles in opposite corners.
  3. All four sides are the equal short sides, and every corner is a right angle.

Answer: A square

Exam-day checklist

  • Match edges of the same length.
  • Count squares (area) to check the pieces can fill the shape.
  • Turn pieces in your head - but only flip if allowed.
  • Check there are no gaps or overlaps.

Common mistakes

  • Flipping a piece when only turning is allowed.
  • Ignoring that the areas must add up.
  • Joining edges of different lengths.

Try it yourself

1. How many equilateral triangles with 1 cm sides fit together to make one equilateral triangle with 2 cm sides?

Show answer

4

Doubling the side length makes the area 4 times bigger: 3 point up and 1 points down.

2. A shape of 12 squares is split into three pieces. Two pieces have 5 and 4 squares. How many squares are in the third piece?

Show answer

3

12 − 5 − 4 = 3.

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