In a rectangular parallelepiped, the base is a rhombus with a side of 3 m and an acute angle of 60 °.

In a rectangular parallelepiped, the base is a rhombus with a side of 3 m and an acute angle of 60 °. side edge equal to 4m find the total surface area and volume of the parallelepiped.

To solve this problem, let us denote a rectangular parallelepiped as ABCDA1B1C1D1:

For the total surface of the prism, we will use the formula S = P * H + 2s, where H is the height and P is the perimeter of the base, s is the area of the base.
The height is the side rib and is equal to 4 m.
The perimeter is: P = 3 + 3 + 3 + 3 = 12 m.
We find the area of the rhombus through the formula s = AB ^ 2 * sin60o = 9 * √3 / 2 m2.
Substitute in the formula and get S = 12 * 4 + 2 * 9 * √3 / 2 = 48 + 9√3 m2.
Volume formula V = s * H = = 9 * √3 / 2 * 4 = 18√3 m3.