Trapezoid area ABCD = 26 BE, CF – heights, point K – midpoint BC, FD = 2BK, BK = 2AE. Find the area of a triangle CEK

univerkov | October 14, 2021 | education

Let the length of the segment ВK = X cm, then BC = 2 * X cm, DF = 2 * X cm, AE = X / 2 cm.

Quadrilateral BCFE rectangle, then ЕF = BC = 2 * X cm.

Base length AD = AE + EF + DF = X / 2 + 2 * X + 2 * X = 4.5 * X cm.

The area of the trapezoid is: (AD + BC) * BE / 2 = 6.5 * X * BE = 26 cm2.

BE = 26 / X * 6.5 = 4 / X cm.

The ABE triangle is rectangular, then Save = BE * AE / 2 = (4 / X) * (X / 2) / 2 = 8/2 = 4 cm2.

Answer: The area of triangle ABE is 4 cm2.

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