# Find the side surface of the rectangle and its volume, taking into account that the sides of the base are 2 cm and 7 cm

**Find the side surface of the rectangle and its volume, taking into account that the sides of the base are 2 cm and 7 cm, the smaller diagonal of the parallelepiped is 8 cm and one of the corners of the base is 60 degrees.**

We construct the diagonal BD and, by the cosine theorem, determine its length.

BD ^ 2 = AB ^ 2 + AD ^ 2 – 2 * AB * AD * Cos60 = 4 + 49 – 2 * 2 * 7 * (1/2) = 39.

ВD = √39 cm.

Since the parallelepiped is straight, the triangle BB1D is rectangular, then BB1 ^ 2 = DB1 ^ 2 – BD ^ 2 = 64 – 39 = 25.

BB1 = 5 cm.

Determine the area of the lateral surface of the parallelepiped.

Sside = Ravsd * BB1 = 2 * (2 + 7) * 5 = 90 cm2.

Determine the area of the base of the parallelepiped.

Sbn = AB * AD * Sin60 = 2 * 7 * √3 / 2 = 7 * √3 cm2.

Then V = Ssc * BB1 = 7 * √3 * 5 = 35 * √3 cm3.

Answer: The lateral surface area is 90 cm2, the volume is 35 * √3 cm3.