At the base of the straight prism lies a parallelogram with sides 4 and 8 and an acute angle of 60 degrees.

univerkov | May 2, 2021 | education

At the base of the straight prism lies a parallelogram with sides 4 and 8 and an acute angle of 60 degrees. The diagonal of the prism makes an angle of 30 degrees with the base plane. Find the area of the lateral surface of the prism.

In triangle ABD, by the cosine theorem, we define the length of the side BD.

BD ^ 2 = AD ^ 2 + AB ^ 2 – 2 * AD * AB * Cos60 = 64 + 16 – 2 * 8 * 4 * (1/2) = 80 – 32 = 48.

AC = 4 * √3 cm.

From the right-angled triangle DBB1, we determine the length of the leg BB1.

BB1 = VD * tg30 = 4 * √3 * (1 / √3) = 4 cm.

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

Sside = P * BB1, where P = the perimeter of the base of the prism.

Sside = (8 + 4 + 8 + 4) * 4 = 96 cm2.

Answer: The lateral surface area is 96 cm2.

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