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5

Part of 2001 Czech And Slovak Olympiad IIIA

Problems(1)

isosceles trapezoid, sides wanted, area given

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2001 p5

2/11/2020
A sheet of paper has the shape of an isosceles trapezoid C1AB2C2C_1AB_2C_2 with the shorter base B2C2B_2C_2. The foot of the perpendicular from the midpoint DD of C1C2C_1C_2 to AC1AC_1 is denoted by B1B_1. Suppose that upon folding the paper along DB1,ADDB_1, AD and AC1AC_1 points C1,C2C_1,C_2 become a single point CC and points B1,B2B_1,B_2 become a point BB. The area of the tetrahedron ABCDABCD is 6464 cm3^3 . Find the sides of the initial trapezoid.
geometrytrapezoidIsosceles Trapezoidarea