Trapezium

A trapezium is a four-sided shape with one pair of parallel sides. That is in British English. In American English this shape is called a trapezoid, and the word trapezium usually means a four-sided shape with no parallel sides at all.^[1] The same word therefore describes two shapes, the same shape has two words, and geometry teachers on either side of the Atlantic have agreed never to meet, like the sides.

A trapezium is often described as a triangle with the top taken off for safety.

Parallel sides

The two parallel sides of a trapezium will never meet, however far they are extended. In 1958 a survey team extended them for 400 miles across open country to make sure. They did not meet, and the team had to walk back.^[2]

Area

The area of a trapezium is half the sum of the parallel sides multiplied by the height. Every pupil is taught this, and most will not meet another trapezium until the day they have to teach it.

In everyday life

• Lampshades, viewed from the side.
• Handbags.
• Slices of cake cut by someone who was nervous.
• Flat-topped mountains that gave up being triangles.

See also

• Circle – no sides, no arguments
• Mountain – a trapezium that kept its point

References

1. Quad, Q. (1988). Four Sides, Two Opinions. Atlantic Press.
2. Parallel, P. & Parallel, P. (1958). “They Didn’t Meet”. Unrelated.