Find the sum of the areas of all the faces of a rectangular parallelepiped if its dimensions are 5cm 2cm 3cm.

The sum of the areas of all the faces of a rectangular parallelepiped is the area of its surface, which consists of six faces in the shape of rectangles. The opposite faces of the parallelepiped are equal, therefore their areas are equal.

Given:

Length – 5 cm.

Width – 2 cm.

Height – 3 cm.

Find: Sпов. -?

Solution:

Since a parallelepiped is constructed from 3 pairs of equal rectangles, then its Sпов. = 2 (S1 + S2 + S3), where S1, S2, S3 are the areas of different (different) faces.

1) S1 = a * b = 5 * 2 = 10 (cm ^ 2).

2) S2 = a * c = 5 * 3 = 15 (cm ^ 2).

3) S3 = b * c = 2 * 3 = 6 (cm ^ 2).

4) Sпов. = 2 (10 + 15 + 6) = 2 * 31 = 62 (cm ^ 2).

Answer: 62 cm ^ 2.