In an isosceles trapezoid ABCD with a large base AD, the height BH divides the base AD into segments
| May 4, 2021 | education
In an isosceles trapezoid ABCD with a large base AD, the height BH divides the base AD into segments 3.5 cm and 8.5 cm. Find the bases of this trapezoid.
The larger base of the trapezoid is equal to the sum of the segments into which the height of the VN divides this base.
AD = AH + HD = 3.5 + 8.5 = 12 cm.
The height of an isosceles trapezoid divides, at the point of intersection, the base into two segments, the smaller of which is half the difference between the bases of the trapezoid.
AH = (AD – BC) / 2.
3.5 = (12 – BC) / 2.
BC = 12 – 7 = 5 cm.
Answer: BC = 5 cm, AD = 12 cm.
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