In a straight prism ABCA1B1C1 Angle BAC = 30 degrees, angle ACB1 = 90 degrees

| April 18, 2021 | education

In a straight prism ABCA1B1C1 Angle BAC = 30 degrees, angle ACB1 = 90 degrees AB = 8 cm CC1 = 5 cm Find the area of the lateral surface of the prism.

According to the condition, the angle ACB1 = 90. Since CB belongs to the plane CC1B1B, which is perpendicular to the plane of the base, and the segment BC is the projection of CB1 onto the plane of the base, then BC is perpendicular to AC, and triangle ABC is rectangular with angle A = 30. Then the leg BC lies opposite the angle 30, BC = AB / 2 = 4 cm. AC ^ 2 = AB ^ 2 – BC ^ 2 = 64 – 16 = 48.

AC = 4 * √3 cm.

Determine the perimeter of the base.

P = (AB + BC + AC) = 8 + 4 + 4 * √3 = 12 + 4 * √3 cm.

Let us determine the area of the lateral surface.

Side = P * CC1 = (12 + 4 * √3) * 5 = 60 + 20 * √3 = 20 * (3 + √3) cm2.

Answer: The lateral surface area is 20 * (3 + √3) cm2.



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