The base of the straight prism ABCA1B1C1 is a triangle ABC, in which AB = BC = 4 m, AC = 6m. The side edge of the prism is 3m. Find the perimeter of the section through vertices A, C, and B1.
Since the prism is straight, its lateral faces are rectangles, and their diagonals AB1 and CB1 form right-angled triangles.
In a right-angled triangle ABB1, by the Pythagorean theorem, we define the hypotenuse AB1.
AB1 ^ 2 = AB ^ 2 + BB1 ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25.
AB1 = 5 cm.
Since AB = BC, then CB1 = AB1 = 5 cm.
Determine the perimeter of the AB1C section.
Rav1s = AB1 + CB1 + AC = 5 + 5 + 6 = 16 cm.
Answer: The perimeter of the section is 16 cm.
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