How do you find the length of the median of a trapezoid when just one base and the 2 legs are given?

Question

For example, given trapezoid CHAD with CH = 12, HK = 9, WD = 7, and median WK. What is the measure of WK?

For example, given trapezoid CHAD with CH = 12, HK = 9, WD = 7, and median WK. What is the measure of WK? By the way, I am referring to the american trapezoid (a quadrilateral with only one pair of sides).

In the sample problem given (from homework), the only other information given was that the measure of angle D = 73 (degrees), as well as a diagram. But the only thing I can observe from the diagram is that CH is the smaller base and DA is the bigger base. If it helps, it is also obvious that the leg HA is 18 and the leg CD is 14.

Answer 1

Look at the smaller trapezoid CHKW, where CH is the smaller base and WK is now the opposite base. Draw an altitude from point H to WK, and call the intersection T. You now have rectangle CHTW, which has sides of length 12 (like CH) and 7 (like CW), and triangle HKT, which has a hypotenuse of 9 (HK) and a leg of length 7 (HT, which is congruent to WD). This leaves the unknown TK. The Pythagorean theorem lets us calculate the length as sqrt(9^2 - 7^2) = sqrt(81 - 49) = sqrt(32) = 4*sqrt(2). The median WK is just the segments WT and TK taken together, and we know that WT has length 12 and TK has length 4*sqrt(2), so the answer is 12 + 4*sqrt(2).

Answer 2

A median of a trapezoid connects the midpoints of the non-parellel sides. It is parallel to the parallel sides, and is the average of the two bases.


Your problem has insufficient information. I could make two trapezoids that meets those criteria, with different median lengths. There must be a picture associated with your (homework) problem.

Answer 3

Medians are just for triangles, I don't know what you're refering to