The height of the correct prism ABCDA1B1C1D1 is 10 cm. The base side of the prism is 12 cm. Calculate the perimeter of the prism section by the plane containing line AB and the midpoint of the edge CC1.
Since the prism is correct, there is a square with a side of 12 cm at its base.
The section containing the straight line AB and the midpoint of the edge CC1 is a rectangle ABHР, which has two sides with the sides of the base of the prism, and the other two are hypotenuses of right-angled triangles.
Since point H is the middle of the edge CC1, then point P is the middle of the edge DD1.
Then DR = DD1 / 2 = 10/2 = 5 cm.
From the right-angled triangle APD we define the hypotenuse AP.
AP ^ 2 = AD ^ 2 + AР ^ 2 = 144 + 25 = 169.
AР = BH = 13 cm.
Determine the perimeter of the section.
Ravnr = 2 * (AR + AB) = 2 * (13 + 12) = 50 cm.
Answer: The perimeter of the section is 50 cm.
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