The side of an isosceles trapezoid is 10, and the bases are 8 and 20. Find the height of the trapezoid.
| May 5, 2021 | education
ABCD is an isosceles trapezoid, AD = 20, BC = 8, CD = AB = 10, CH and BM are heights.
The heights of an isosceles trapezoid divide its base into three segments: AM, MH, HD.
In this case, AM = HD, MH = BC = 8.
Find the length of the segment HD:
HD = (AD – MH) / 2 = (20 – 8) / 2 = 6.
Consider the triangle CHD. Since CH is height, the triangle is rectangular.
Let’s apply the Pythagorean theorem to find the length of CH:
CH ^ 2 = CD ^ 2 – HD ^ 2.
CH = √ (CD ^ 2 – HD ^ 2) = √ (100 – 36) = √64 = 8.
Answer: CH = 8.
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