Math CentralQuandaries & Queries


Question from Hannah, a student:

A designer vase has the shape of a truncated, square-based pyramid. The base of the vase is a square with a side length of 15 cm. The area of the square opening is 70.56 cm2. Each of the four sides is a trapezium with slant sides 9 cm long. Find (to the nearest square centimetre) the total surface area of the vase.

Hi Hannah,

The words trapezium and trapezoid meanings in Canada and the United States which are contradictory to their meanings in the rest of the world. Look them up in Wikipedia to see what I mean. Since you are in Australia the word trapezium is appropriate here.

The area of the base is easy to calculate and the top is an open, thus to complete the solution you only need to calculate the areas of the four congruent sides. These are isosceles trapeziums. The area of a trapezium can be found in my response to an earlier question (notice I called it a trapezoid).Since you know the area of the square opening at the top of the vase you can find the length of the shorter of the two parallel sides of the trapezium. To find the distance between the parallel sides you can use Pythagoras' theorem.


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