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

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.