In an isosceles trapezoid, the height drawn from the top of the obtuse angle divides the larger base into 6 cm and 30 cm segments. Find the bases of the trapezoid.
Determine the length of the AD base.
AD = AН + DH = 6 + 30 = 36 cm.
According to the property of the height of an isosceles trapezoid, the height divides the larger base into two segments, the smaller of which is equal to the half-difference of the bases, and the larger segment from the half-sum.
AH = (AD – BC) / 2 = 6 cm.
36 – BC = 12.
BC = 36 – 12 = 24 cm.
Answer: The bases of the trapezoid are 24 cm and 36 cm.
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