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Science project idea

Trapezium area from two copies that form a parallelogram

Two identical trapeziums, one turned upside down, fit together into a parallelogram whose base is the sum of the two parallel sides. This shows that the area of a trapezium is half of the sum of the parallel sides times the height.

Make it yourself8 numbered steps, the materials and the science, all free.Go to the stepsGet a ready-made kitReady-made models, kits and spare parts in the store under Maths.Browse MathsAsk on WhatsAppAsk the head office whether a model or kit for this idea is available.Send a message

What it shows

Two identical trapeziums, one turned upside down, fit together into a parallelogram whose base is the sum of the two parallel sides. This shows that the area of a trapezium is half of the sum of the parallel sides times the height.

The science

A trapezium has two parallel sides, a and b, and a height h between them. Two copies joined with one rotated by 180 degrees form a parallelogram whose base is a plus b and whose height is h. The parallelogram has an area (a + b) times h, so one trapezium has half of this, giving area = 1/2 (a + b) h. The same formula works for every trapezium, including the isosceles one and the right-angled one.

Materials

Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.

  • Thick coloured paper, 2 sheets
  • A ruler
  • Scissors
  • A pencil
  • Glue and a chart sheet
  • Squared paper
  • A set square

Safety

For this project: An adult should help young children with scissors.

Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.

All the safety rules

Step by step

8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.

  1. Draw a trapezium on paper with parallel sides of 10 cm and 6 cm and a height of 5 cm, using the set square to get right angles.

  2. Cut out the trapezium and trace it on a second sheet to make an identical copy, and cut that one out too.

  3. Turn the second copy upside down and slide it next to the first one, matching the slanting sides, to make a parallelogram.

  4. Measure the long base of the parallelogram. It should be 10 + 6 = 16 cm. Check the height of 5 cm.

  5. Calculate the area of the parallelogram: 16 times 5 = 80 square cm.

  6. Find the area of one trapezium as half of it, 40 square cm, and check by the formula 1/2 times (10 + 6) times 5.

  7. Check by laying one trapezium on squared paper and counting the squares.

  8. Repeat with a trapezium with different sides, and stick the models on the chart with the working.

What you should see

The two trapeziums fit to form a parallelogram and the formula, the doubled model and the square count agree at about 40 square cm.

Viva questions

A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.

1What is the area of a trapezium?

Half the sum of the parallel sides times the height.

2Why do two copies make a parallelogram?

The slanting sides of one fit the other when it is rotated by 180 degrees.

3What does the height mean?

The perpendicular distance between the parallel sides.

4What happens if the two parallel sides are equal?

The shape is a parallelogram and the formula becomes base times height.

Free ebook: Viva Questions for Science Projects

Take it further

Measure a trapezium-shaped field or a sloping window from a photograph and find its area.

Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.

Free ebooks for this project

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