In a rectangular parallelepiped, the length and width are 8m and 2m, and the sum of the areas

In a rectangular parallelepiped, the length and width are 8m and 2m, and the sum of the areas of all its faces is 132m (2). Find the sum of the lengths of all the edges of the parallelepiped.

1. The sum of all the lengths of the parallelepiped is 4 * a + 4 * b + 4 * h, where a is the length, b is the width, h is the height of the parallelepiped.

By the condition of the problem, a = 8 m, b = 2 m, so you need to find the height h.

2. The height h can be found from the formula for the lateral surface area S side. parallelepiped.

S side. = P * h, where P is the perimeter of the base.

3. We only know the total area of ​​all faces of the parallelepiped, which is 132 m ^ 2.

S total = S side. + 2 * S main;

S side. = 132 – 2 * S main. = 132 – 2 * a * b = 132 – 2 * 8 * 2 = 100 m ^ 2.

4. Sides. = P * h whence

h = S side. : P = 100: (2 * a + 2 * b) = 100: 20 = 5 m.

5. Find the sum of the lengths of all edges.

4 * a + 4 * b + 4 * h = 4 * 8 + 4 * 2 + 4 * 5 = 68 m.

Answer: The sum of the lengths of all the edges of the parallelogram is 68 meters