# Two edges of a rectangular parallelepiped extending from one vertex are equal to 48 and 12 diagonal

Two edges of a rectangular parallelepiped extending from one vertex are equal to 48 and 12 diagonal of a parallelepiped is equal to 52 find the surface area and volume of the parallelepiped.

We will use the theorem on the diagonal of a rectangular parallelepiped: the square of the diagonal of a rectangular parallelepiped is equal to the sum of the squares of its three dimensions.

In the drawing: a – length, b – width, c – height, d – diagonal.

d ^ 2 = a ^ 2 + b ^ 2 + c ^ 2.

42 ^ 2 + 12 ^ 2 + c ^ 2 = 52 ^ 2.

2 304 + 144 + c ^ 2 = 2 704.

2,448 + c ^ 2 = 2,704.

c ^ 2 = 2 704 – 2 448.

c ^ 2 = 256.

c = √256.

c1 = 16; c2 = -16 (the second root is not suitable, because c is the height of the box, the value of which cannot be expressed as a negative number).

Find the surface area of ​​the parallelepiped. It has 6 faces, each face is a rectangle. You need to find the areas of each face and add them. The formula can be written like this:

S on top. = 2ac + 2ab + 2bc = 2 x (ac + ab + bc).

S on top. = 2 x (48 x 16 + 48 x 12 + 12 x 16) = 2 x (768 + 576 + 192) = 2 x 1 536 = 3 072.

We find the volume of the parallelepiped by the formula: V = a x b x c.

V = 48 x 12 x 16 = 9 216.

Answer: the surface area of ​​the parallelepiped is 3,072, its volume is 9,216.

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