Math CentralQuandaries & Queries


Question from Martha:

What is the lot size of the following dimensions equivalent to acre.  I know that is is less than an acre.
141.85  x  52.55  x  217.63  x  38.89  x  68.08

Hi Martha. Frequently Asked Question

 Sorry but that isn't enough information to find the area. Here's the rule:

Whenever you have a shape with more than three sides,
the lengths of the sides alone are not enough to determine the area of the shape.

Take a look at the short video on the right (30 seconds).

It shows a five-sided shape with all the lengths of the sides known and unchanging. Yet, the angles are changing and it is the combination of the angles and the sides that determines the shape and area.

Notice how you can construct a very small area or a large area  using the same side lengths!

In order to determine the area, we need a fixed form - that is, the shape cannot change.

That means we need to know the lengths of the diagonals (so that we can break the shape down into triangles) or the angles at the corners. When we have the lengths and the angles, we can determine the area.

Many people make the incorrect assumption that area is based only on the lengths of the sides, but you can see now that more information is needed.

Penny Nom and Stephen La Rocque.

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS