The height of the rectangular parallelepiped is exactly 4 4/5 cm, its length is 3 1/8

The height of the rectangular parallelepiped is exactly 4 4/5 cm, its length is 3 1/8 times its height, and its width is 60% of the length. Calculate the area of the box.

Area of a rectangular parallelepiped:

S = 2 * (ab + bc + ac)

Where:

ab – height;

bc – length;

ac – width.

Let’s find the parameters of the rectangular parallelepiped:

Height ab = 4 4/5 cm.

Length bc = 3 1/8 * 4 4/5 = 24/8 * 24/5 = 576/40 = 14 16/40 = 14 4/10 cm.

Width ac = 30% bc = 0.3 * bc = 3/10 * bc = 3/10 * 576/40 = 1728/400 = 4 128/400 = 4 32/100 = 4 8/25 cm.

Then the area of the rectangular parallelepiped will be:

S = 2 * (ab + bc + ac) = 2 * (4 4/5 + 14 4/10 + 4 8/25) = 2 * (24/5 + 144/10 + 108/25) = 2 * ( 24/5 + 72/5 + 108/25) = 2 * (96/5 + 108/25) = 2 * (480/25 + 108/25) = 2 * 588/25 = 1176/25 = 47 1 / 25 = 47.04 cm2