We give the height BH of the trapezoid.
Since the trapezoid is isosceles, the segment AK is equal to the half-difference of the lengths of the bases.
AK = (AD – BC) / 2 = (15 – 7) / 2 = 4 cm.
In a right-angled triangle ABK, according to the Pythagorean theorem, we determine the length of the leg BK.
BK ^ 2 = AB ^ 2 – AK ^ 2 = 25 – 16 = 9.
BK = 3 cm.
Determine the length of the midline of the trapezoid. РМ = (АD + ВС) / 2 = (15 + 7) / 2 = 11 cm.
Answer: The height of the trapezoid is 3 cm, the middle line is 11 cm.
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