In a regular hexagonal prism ABCDEFA1B1C1D1E1F1 all edges are equal to 2. Find the cross-sectional

univerkov | September 25, 2021 | education

In a regular hexagonal prism ABCDEFA1B1C1D1E1F1 all edges are equal to 2. Find the cross-sectional area passing through vertices A, C and D1.

Section AF1CD1 is a rectangle.

In a right-angled triangle DCD1, according to the Pythagorean theorem, we determine the length of the hypotenuse CD1.

CD1 ^ 2 = D ^ 2 + DD1 ^ 2 = 4 + 4 = 8.CD1 = √8 = 2 * √2 cm.

The segment AC is the base of the isosceles triangle ABC with angles ABC = 120.

Then, by the cosine theorem, AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos120 = 4 + 4 – 2 * 2 * 2 * (-1/2) = 8 + 4 = 12.

AC = 2 * √3 cm.

Determine the cross-sectional area. Ssection = CD1 * AC = 2 * √2 * 2 * √3 = 4 * √6 cm2.

Answer: The cross-sectional area is 4 * √6 cm2.

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