The side surface of a regular quadrangular prism is 720 A total surface 1008 centimeters Find the height of the prism.

A regular quadrangular prism is a hexagon, the bases of which are two equal squares, and the side faces (there are 4 of them) are equal rectangles.

On him:

ABCD and MNOP are bases (equal squares). Means: AB = BC = CD = AD = a see.

ADPM, ABNM? BCON, СDPO – side faces (equal rectangles). Hence, AM = BN = CO = DP = h see.

The area of ​​each base of the prism is: (a x a) cm2.

The area of ​​each face is equal to: (a x h) cm2.

The total surface area of ​​the prism is the sum of the areas of the two bases and four side faces, that is, it is equal to: 4 x a x h + 2 x a x a. This area is conditionally equal to 1008 cm2.

Thus: 4 x a x h + 2 x a x a = 1008 (equation 1).

The lateral surface area of ​​the prism is the sum of the areas of all the lateral faces. This means that it is equal to 4 x a x h, which by condition is 720 cm2. We get:

4 x a x h = 720 (equation 2).

In equation 1, instead of 4 x a x h, substitute 720.

720 + 2 x a x a = 1008.

Solving the new equation:

2 x a x a = 1008 – 720.

2 x a x a = 288.

a x a = 288: 2.

a x a = 144.

a = 12.

Substitute the found value a into equation 2:

4 x a x h = 720.

4 x 12 x h = 720.

48 x h = 720.

h = 720: 48.

h = 15.

Answer: The height of the prism is 15 cm.

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