The height of a regular prism MPRM1P1K1 is 12 cm. The side of its base is 6 out of three roots.

| May 2, 2021 | education

The height of a regular prism MPRM1P1K1 is 12 cm. The side of its base is 6 out of three roots. Calculate the perimeter of the prism section by a plane containing straight line PP1 midpoint of edge MK.

Since the prism is correct, at its base lies an equilateral triangle with a side of 6 * √3 cm.

The desired section is a rectangle РР1NA, which has two sides of the lateral edges of the prism, and the other two are the medians of an equilateral triangle, which are also the heights of an equilateral triangle.

The height of an equilateral triangle is: h = РK = P1H = a * √3 / 2, where a is the length of the side of the triangle.

РK = P1H = 6 * √3 * √3 / 2 = 9 cm.

Determine the perimeter of the section.

Rrr1nk = 2 * (РР1 + РK) = 2 * (12 + 9) = 42 cm.

Answer: The perimeter of the section is 42 cm.



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