In an inclined triangular prism, the side edge is 10 cm. The areas of the two side faces are 30 cm2 and 40 cm2

| May 19, 2021 | education

In an inclined triangular prism, the side edge is 10 cm. The areas of the two side faces are 30 cm2 and 40 cm2, the angle between them is straight. The area of the lateral surface of the prism is …

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

Since, by condition, the side faces АА1С1С and СС1В1В are perpendicular, the triangle А1МК is rectangular.

Let the area of ​​the side face of АА1В1В be equal to 40 cm2, then the area of ​​the CC1В1В face perpendicular to it is equal to 30 cm2.

Determine the heights A1M and MK of the side faces.

A1M = Saa1c1c / CC1 = 40/10 = 4 cm.

MK = Scc1v1v / CC1 = 30/10 = 3 cm.

Then, by the Pythagorean theorem, in a right-angled triangle A1MK, A1K ^ 2 = A1M ^ 2 + MK ^ 2 = 16 – 9 = 25.

A1K = 5 cm.

Then Pa1mk = 3 + 4 + 5 = 12 cm.

Sside = Pa1mk * CC1 = 12 * 10 = 120 cm2.

Answer: The lateral surface area is 120 cm2.



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