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

A rectangular parallelepiped is a polyhedron built from six faces, each of which is a rectangle. The opposite faces of the box are equal. A rectangular parallelepiped has 12 edges and 8 vertices. Three edges extending from one vertex are called the dimensions of the parallelepiped or its length, height and width.

The sum of the areas of all the faces of a rectangular parallelepiped is called its surface area.

Given:

a = 5 cm;

b = 2 cm;

c = 3 cm.

Find: Sпов.

Solution:

Since the opposite faces are equal, then:

Spov. = 2 * S1 + 2 * S2 + 2 * S3 = 2ab + 2ac + 2bc = 2 * 5 * 2 + 2 * 5 * 3 + 2 * 2 * 3 = 20 + 30 + 12 = 62 (cm ^ 2).

Answer: 62 cm ^ 2.