Trapezoid midsegment length

0:00- [Instructor] Here we are asked what is the length of the side or the segment EF. So that is this right over here that I am highlighting in this blue color. I don't know if you can see it. Maybe I'll do it in a more visible color. Maybe I'll do it in this pink color right over here.

0:17What is the length of that? Pause this video. Have a go at that before we do this together. So the important thing to realize here is this is a trapezoid, and a trapezoid is a quadrilateral that has a pair of parallel sides, and side CD and BA are the parallel sides.

0:36And we call those the bases. And we call the sides that connect them the legs. Now, what's interesting about this is this segment that we're trying to figure out, the length of EF, that, where it intersects the two legs, is exactly at their midpoint. Notice this distance and this distance are the same.

0:56This distance and this distance are the same. And so what we know is that this is known as the mid segment. And the mid segment, which intersects the two legs right at their midpoint, is also equal to the average length of the bases. So we really just have to figure out the average of 13 centimeters and 4 centimeters.

1:15And that of course is going to be 13 centimeters plus 4 centimeters divided by 2, which is equal to 17 centimeters, divided by 2, which is equal to 8.5 centimeters. And we are done.