# In an isosceles trapezoid, the side is 25cm, the diagonal is 30cm, and the smaller base is 11cm.

September 29, 2021 | education

| **In an isosceles trapezoid, the side is 25cm, the diagonal is 30cm, and the smaller base is 11cm. Find the height of the trapezoid.**

By Heron’s theorem, we determine the area of the triangle ABC.

S = √p * (p – AC) * (p – AB) * (p – BC), where p is the semiperimeter of the triangle.

P = (AB + BC + AC) = (25 + 11 + 30) / 2 = 33 cm.

S = √33 * (33 – 30) * (33 – 25) * (33 – 11) = √33 * 3 * 8 * 22 = √17424 = 132 cm2.

Let’s define the area of the triangle ABC through the height and base.

S = BC * AH / 2 = 11 * AH / 2 = 132.

AH = 132 * 2/11 = 24 cm.

Answer: The height of the trapezoid is 24 cm.

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