The base of a straight parallelepiped is a rhombus with diagonals 24 and 10. The diagonal of the side face is √178.

| February 16, 2021 | education

The base of a straight parallelepiped is a rhombus with diagonals 24 and 10. The diagonal of the side face is √178. Find the area full of the parallelepiped’s surface.

Knowing the diagonals of the rhombus at the base of the parallelepiped, we determine its area.

Sbn = AC * ВD / 2 = 24 * 10/2 = 120 cm2.

The diagonals of the rhombus are perpendicular and are divided in half at point O, then in a right-angled triangle СOD, according to the Pythagorean theorem, we determine the length of the hypotenuse of the СD.

СD ^ 2 = OС ^ 2 + OD ^ 2 = 144 + 25 = 169.

СD = 13 cm.

Since the parallelepiped is straight, the triangle SDD1 is rectangular, then DD1 ^ 2 = СD1 ^ 2 – СD ^ 2 = 178 – 169 = 9.

DD1 = 3 cm.

Let us determine the area of the lateral surface. Sside = Rosn * DD1 = 4 * 13 * 3 = 156 cm2.

Then Sпов = 2 * Sсн + Sside = 2 * 120 + 156 = 396 cm2.



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