The base of the straight prism ABCDA1B1C1D1 is the parallelogram ABCD with sides of 4 and 8 cm

univerkov | August 12, 2021 | education

The base of the straight prism ABCDA1B1C1D1 is the parallelogram ABCD with sides of 4 and 8 cm, the angle BAD = 60 degrees. The diagonal B1D of the prism makes an angle of 30 degrees with the base plane. Find the area of the lateral surface of the prism.

Consider the triangle ABD and define the side BD by the cosine theorem.

BD² = AB² + AD² – 2 * AB * AD * Сos60 = 16 + 64 – 2 * 4 * 8 * 0.5 = 80 – 32 = 48.

ВD = 4 * √3 cm.

Consider a right-angled triangle BB1D and determine the height of the prism BB1.

tgВДВ1 = BB1 / BD.

BB1 = tg30 * BD = (√3 / 3) * 4 * √3 = 4 cm.

Let us determine the area of the lateral surface of the prism:

S side = P * h = (AB + BC + CD + AD) * BB1 = 24 * 4 = 96 cm2.

Answer: S side = 96 cm2.

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