The bases of the rectangular trapezoid are 6 cm and 8 cm, and the height is 5 cm.

The bases of the rectangular trapezoid are 6 cm and 8 cm, and the height is 5 cm. Find the length of the segment connecting the midpoints of the bases.

Let us draw the height MH from the middle of the base of the BC to the base of AD.

In the formed rectangle BMHA, side AH = BM = BC / 2 = 6/2 = 3 cm.

Then the segment НК = АD – КD – АН = 8 – 4 – 3 = 1cm.

Then from the triangle MHK, by the Pythagorean theorem, we determine the length of the hypotenuse MK.

MK ^ 2 = MH ^ 2 + HK ^ 2 = 5 ^ 2 + 1 ^ 2 = 26.

MK = √26 cm.

Answer: The length of the segment connecting the midpoints of the bases is 26 cm.