The width of the rectangular parallelepiped is 14 cm, it is half the length, but 4 cm

The width of the rectangular parallelepiped is 14 cm, it is half the length, but 4 cm more than the height. Find the sum of the lengths of all edges and the surface area.

1) Since the width of the rectangular parallelepiped is half the length, the length will be equal to:

14 * 2 = 28 cm.

2) The width of the rectangular parallelepiped is 4 cm more than the height, so the height is equal to:

14 – 4 = 10 cm.

3) The sum of the lengths of all edges is found by the formula:

4 * a + 4 * b + 4 * c,

where a = 28 cm – length,

b = 14 cm – width,

c = 10 cm – height.

4 * 28 = 112 cm – the sum of the lengths of the parallelepiped;

4 * 10 = 40 cm – the sum of the heights of the parallelepiped;

4 * 14 = 56 cm – the total value of the width of the parallelepiped;

112 + 40 + 56 = 208 cm.

4) The surface area of ​​a rectangular parallelepiped is equal to twice the sum of the areas of the three faces of this parallelepiped:

S = 2 * (a * b + b * c + a * c);

S = 2 * (28 * 14 + 14 * 10 + 28 * 10) = 2 * (392 + 140 + 280) = 1 624 cm2.