In an inclined triangular prism, the two side faces are mutually perpendicular. Their common rib, which is 12 cm

| March 1, 2021 | education

In an inclined triangular prism, the two side faces are mutually perpendicular. Their common rib, which is 12 cm and 35 cm apart from the other two side ribs, is 24 cm. Find the lateral surface area.

From the vertex A1 of the prism, construct the perpendiculars A1M to the edge CC1 and A1K to the edge BB1.

Since, by condition, the side faces АА1С1С and CC1В1В are perpendicular, the triangle А1МК is rectangular.

The A1M leg is the distance between the AA1 and CC1 lateral ribs, according to the condition, A1M = 35 cm, the MK leg is the distance between the CC1 and BB1 ribs, MK = 12 cm.

In a right-angled triangle A1KM, according to the Pythagorean theorem, A1K ^ 2 = A1M ^ 2 + MK ^ 2 = 1225 + 144 = 1369.

A1K = 37 cm.

Section A1MK is perpendicular to the side face of CC1B1B. The section perimeter is equal to:

Rsech = (A1M + MK + A1K) = 35 + 12 + 37 = 84 cm.

Then S side = Rsech * CC1 = 84 * 24 = 2016 cm2.

Answer: The lateral surface area is 2016 cm2.



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