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How many trapezoids can you count?
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Let’s begin by recalling that a trapezoid is defined as a quadrilateral with one pair of parallel sides.
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In some countries, this is often referred to as a trapezium.
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As we answer this question, which is quite like a puzzle, we can observe that we have in fact got three parallel sides.
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Using the highest and the lowest parallel sides, there is one trapezoid created by the exterior lines in this figure.
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Let’s see how many other ones we can find.
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Given that we know that this middle line is also a parallel side, then we can create a second trapezoid.
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And then if we use the middle and the lower parallel sides, then we can see a third trapezoid.
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Let’s pause for a second to see the three trapezoids that we’ve already found.
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In each case, we can see that they form a quadrilateral with one pair of parallel sides.
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The question is, are there any more?
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Let’s return to the original figure.
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And this time, let’s see if we can make any trapezoids that make use of this diagonal of the larger trapezoid.
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But if we use this with the right leg of the largest trapezoid, then we’d find that we’d only create a triangle.
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However, if we used just part of this leg and part of the diagonal, we find that there’s a fourth trapezoid.
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There is in fact another trapezoid that can be made using part of the diagonal of the largest one.
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It’s this one.
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Therefore, we’ve found five different trapezoids.
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And in each case, they have a pair of parallel sides.
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It doesn’t matter that in the last two we found the nonparallel sides were of a different length.
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It would still count as a trapezoid.
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As there are no other trapezoids in this figure, then our answer would be five.