Question Video: Counting the Number of Trapezoids in a Shown Figure Mathematics

How many trapezoids can you count?

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Video Transcript

How many trapezoids can you count?

Let’s begin by recalling that a trapezoid is defined as a quadrilateral with one pair of parallel sides. In some countries, this is often referred to as a trapezium. As we answer this question, which is quite like a puzzle, we can observe that we have in fact got three parallel sides. Using the highest and the lowest parallel sides, there is one trapezoid created by the exterior lines in this figure. Let’s see how many other ones we can find. Given that we know that this middle line is also a parallel side, then we can create a second trapezoid. And then if we use the middle and the lower parallel sides, then we can see a third trapezoid.

Let’s pause for a second to see the three trapezoids that we’ve already found. In each case, we can see that they form a quadrilateral with one pair of parallel sides. The question is, are there any more? Let’s return to the original figure. And this time, let’s see if we can make any trapezoids that make use of this diagonal of the larger trapezoid. But if we use this with the right leg of the largest trapezoid, then we’d find that we’d only create a triangle. However, if we used just part of this leg and part of the diagonal, we find that there’s a fourth trapezoid. There is in fact another trapezoid that can be made using part of the diagonal of the largest one. It’s this one.

Therefore, we’ve found five different trapezoids. And in each case, they have a pair of parallel sides. It doesn’t matter that in the last two we found the nonparallel sides were of a different length. It would still count as a trapezoid. As there are no other trapezoids in this figure, then our answer would be five.

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