In a regular triangular prism, the lengths of all sides = 2 cm. Find the S section drawn through the side edge

univerkov | March 1, 2021 | education

In a regular triangular prism, the lengths of all sides = 2 cm. Find the S section drawn through the side edge and the middle of the opposite side of the base.

The sectional area is a rectangle АА1Н1Н, two sides of which are segments АА1 and НН1 equal in length to the lateral edge of the prism. AA1 = HH1 = 2 cm, and the other two medians of the triangles at the base of the prism.

Since the prism is regular, the triangles ABC and A1B1C1 are equilateral, then AH = A1H1 = AB * √3 / 2 = 2 * √3 / 2 = √3 cm.

Then the cross-sectional area is equal to: Ssection = АА1 * АН = 2 * √3 cm2.

Answer: The cross-sectional area is 2 * √3 cm2.

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