# In a rectangular parallelepiped, the sides of the base are 15cm and 8cm. The diagonal

In a rectangular parallelepiped, the sides of the base are 15cm and 8cm. The diagonal of the parallelepiped makes an angle of 45 degrees with the base plane. Find the area of the side and full surface of a parallelepiped

The diagonal of a parallelepiped is the hypotenuse of a rectangular triangle, the legs of which are equal to the height of the parallelepiped and the diagonal of its base.

Using the Pythagorean theorem, we find what the diagonal of the base is equal to:

15² + 8² = x²,

x² = 225 + 64,

x² = 289,

x = 17 (cm).

According to the condition of the problem, the diagonal is inclined to the plane of the base at an angle of 45 degrees, which means that the height of the parallelepiped and the diagonal of the base are the legs of an isosceles triangle. Thus, the height is also 17 cm.

The lateral surface area will be equal to:

S = 2 * 8 * 17 + 2 * 15 * 17 = 272 + 510 = 782 (cm²).

The total surface area is:

S = 782 + 2 * 8 * 15 = 782 + 240 = 1022 (cm²).

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