Question Video: Finding the Length of the Middle Base of a Trapezoid given Its Parallel Bases Mathematics

Find the length of the middle base of a trapezoid whose parallel bases are 107 cm and 246 cm.

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Video Transcript

Find the length of the middle base of a trapezoid whose parallel bases are 107 centimeters and 246 centimeters.

Let’s begin this question by seeing if we can model what this trapezoid may look like. As this is a trapezoid, we know that there’ll be one pair of parallel sides. We often refer to these as the bases of the trapezoid. We can show that the smaller base would be 107 centimeters and the larger base would be 246 centimeters.

We’re asked to find the length of the middle base of this trapezoid and the middle base is often called the midsegment. The midsegment of a trapezoid is the line that joins the midpoints of the two nonparallel sides. In order to find the length of this midsegment or middle base, we’ll need to remember an important fact about the midsegment of a trapezoid. And that is that the length of the midsegment of a trapezoid is half the sum of the lengths of the two parallel sides.

In other words, if we add the length of the top base and the lower base together and then divide it by two or halve it, then we’d find the length of this midsegment. As we know the values for the length of the two bases, then we add these together, 107 plus 246 and then divide by two, which gives us a value of 176.5. We know that the length units will still be in centimeters. And so we have our answer that the length of the midsegment or middle base is 176.5 centimeters.

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