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.