Find the side edge of a regular quadrangular prism if the side of its base is 15 and the surface area is 930.

Find the area of ​​the base of a regular quadrangular prism, which is a square:

Sb = 15² = 225.

Let us find the sum of the areas of both bases of the prism:

225 * 2 = 450.

Let us find the area of ​​the lateral surface of a regular quadrangular prism. To do this, subtract the area of ​​its bases from the total surface area:

Sbp = Spp – 2Sosn = 930 – 450 = 480.

In total, the quadrangular prism has 4 side faces. Let’s find the area of ​​one of them:

Sgr = 480/4 = 120.

On the other hand, the area of ​​the side face is:

Sgr = ab, where a is the side of the base, b is the side edge.

Hence the side edge is equal to:

b = Sgr / a.

Find the side edge:

b = 120/15 = 8.

Answer: the side edge of a regular quadrangular prism is 8.