In an inclined triangular prism ABCA1B1C1, the angle between the faces AA1CC1 and CC1BB1 is straight

| January 6, 2021 | education

In an inclined triangular prism ABCA1B1C1, the angle between the faces AA1CC1 and CC1BB1 is straight. find the area of the side surface of the pyramid if the side edge is 5 cm, and the areas of the faces АА1ВВ1 and CC1ВВ1 are 130 cm2 and 50 cm2, respectively.

From the vertex A1 of the prism, construct the perpendiculars A1M to the edge CC1 and A1K to the edge BB1.
By condition, the side faces АА1С1С and СС1В1В are perpendicular, then triangle А1МК is rectangular.
The area АА1В1В, by condition, is equal to 130 cm2, then we determine the length of the height А1К of the side face.
A1K = Saa1b1v / BB1 = 130/5 = 26 cm.
The height of the side face CC1B1C will be equal to: MK = Scc1v1v / CC1 = 50/5 = 10 cm.
According to the Pythagorean theorem, in a right-angled triangle A1MK, A1M2 = A1K2 – MK2 = 676 – 100 = 576.
A1M = 24 cm.
Then Pa1mk = 26 + 24 + 10 = 60 cm.
Side = Pa1mk * CC1 = 60 * 5 = 300 cm2.
Answer: The lateral surface area is 300 cm2.



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