At the base of the straight prism lies a rhombus with diagonals of 16cm and 30cm, and the diagonal of the side face

| August 7, 2021 | education

At the base of the straight prism lies a rhombus with diagonals of 16cm and 30cm, and the diagonal of the side face of the prism forms an angle of 60 degrees with the base. Find the area of the lateral surface of the prism.

Since at the base of the prism the rhombus, and its diagonals, at the point of intersection are divided in half and intersect at right angles, the triangle AOD is rectangular, AO = AC / 2 = 30/2 = 15 cm, OD = 16/2 = 8 cm.

Then, by the Pythagorean theorem, AD ^ 2 = AO ^ 2 + OD ^ 2 = 225 + 64 = 289.

AD = 17 cm.

Since the prism is straight, the triangle ADD1 is rectangular, then tg36 = DD1 / AD.

DD1 = AD * tg60 = 17 * √3 cm.

Since the lengths of all sides of a rhombus are equal, then Sside = 4 * Saa1d1d = 4 * 17 * 17 * √3 = 1156 * √3 cm2.

Answer: The lateral surface area is 1156 * √3 cm2.



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