Find the surface area of a rectangular parallelepiped if its height is 42 cm

Find the surface area of a rectangular parallelepiped if its height is 42 cm, width is 3 times less than its height and its length is 2 cm more than its width.

1) Find the width of the parallelepiped:

42/3 = 14 (cm)

2) Find the length of the parallelepiped:

14 + 2 = 16 (cm)

The surface area of the entire figure is equal to the sum of the areas of all its faces. The parallelepiped has only 6 faces, the opposite faces are equal and have the same area.

Therefore, we find the area of each face using the rectangle area formula (S = ab), multiply it by two, and sum all the areas. In this way:

42 * 14 * 2 + 14 * 16 * 2 + 16 * 42 * 2 = 1176 + 448 + 1344 = 2968 (cm3) – the area of all faces.

Answer: the surface area is 2968 cm3.