Math CentralQuandaries & Queries


Question from Scott, a student:

How can we calculate this I do not understand?
A trapezium of area 126m^2 has parallel sides of length 3m and 4m. How far apart are the parallel sides?

Hi Scott.

The area of a trapezium is (a+b)h/2, where a and b are the lengths of the parallel sides and h is the height, or distance between the parallel sides.

So you know: 126 = (3+4)h/2. Solve for h.

Stephen La Rocque.

Hi Scott,

I just wanted to add a footnote to Stephen's response that if you are looking up information on a trapezium, either in a dictionary or on the web, you need to be careful. Here is part of the entry in Wikipedia for trapezoid

A trapezoid (in North America) or trapezium (in Britain and elsewhere) is a quadrilateral, which is defined as a shape with four sides, which has one set of parallel sides. Some authors define it as a quadrilateral having exactly one set of parallel sides, so as to exclude parallelograms, which otherwise would be regarded as a special type of trapezoid.

The exactly opposite kind of quadrilateral, that is, one which does not have any parallel sides, is called a trapezium in North America and a trapezoid in Britain and elsewhere.


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