# The base of the straight prism ABCA1B1C1 is a triangle ABC, in which AB = BC = 4 m, AC = 6m.

March 29, 2021 | education

| **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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