The height of the rectangle of the parallelepiped is 2 cm; the length of the lower edge is 6 cm in the area

The height of the rectangle of the parallelepiped is 2 cm; the length of the lower edge is 6 cm in the area of this edge is 24 cm2. Calculate the area of the remaining faces of the parallelepiped.

Decision.

A rectangular parallelepiped is a polyhedron with six faces, each of which is a rectangle.

The opposite faces of the box are equal. The edges of a parallelepiped meeting at one vertex are mutually perpendicular.

The surface area of ​​a rectangular parallelepiped is:

S = 2 (ab + bc + ac) where a, b, c are the edges of the parallelepiped.

By the condition a = 2, b = 6, c – we find from the condition that the area of ​​a face with a side of 6 cm is equal to 24 cm2. c = 24/6 = 4.

S = 2 * (a * b + b * c + a * c) = (6 * 2 + 6 * 4 + 2 * 4) = 2 * (12 + 24 + 8) = 88.

The area of ​​one surface is already known, so the sum of the areas of the remaining faces:

88 – 24 = 64.

Answer. 64.