ABCD is an isosceles trapezoid, CH is its height. find the base AD if AB = 13m, CH = 12m, BC = 16m.

Since the trapezoid is isosceles, then CD = AB = 13 m, then in a right-angled triangle CDH, according to the Pythagorean theorem, we determine the length of the leg DH.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 169 – 144 = 25.

DН = 5 m.

Let’s draw the height of the ВK trapezoid. Since the trapezoid is isosceles, the segment AK = DH = 5 m.

СВНK is a rectangle, since BC is parallel to AD as the base of the trapezoid, and ВK and CH are perpendicular to the bases, then BC = KH = 16 m.

Determine the length of the base AD. AD = AK + DH + KH = 5 + 5 + 16 = 26 m.

Answer: The length of the base AD is 26 m.