# How many times will the surface area of a regular octagonal prism increase if all its edges are increased by 1.5 times?

a1 = 1.5 * a.

h1 = 1.5 * h

S1 / S2 -?

The surface area S of a regular octagonal prism is determined by the formula: S = 2 * S main + 8 * S side.

The base of a regular octagonal prism is a regular octagon.

The area of ​​a regular octagon is determined by the formula: Sb = 2 * a ^ 2 * (1 + √2).

Sside = a * h.

S1 = 2 * Sbok1 + 8 * Sbok1.

Sosn1 = 2 * a1 ^ 2 * (1 + √2) = 2 * (1.5 * a) ^ 2 * (1 + √2) = 2.25 * 2 * a ^ 2 * (1 + √2) = 2.25 * Sb.

S side1 = a1 * h1 = 1.5 * a * 1.5 * h = 2.25 * a * h = 2.25 * S side.

S1 = 2 * Sbn1 + 8 * Sbok1 = 2 * 2.25 * Sbn + 8 * 2.25 * Sbok = 2.25 * (2 * Sbn + 8 * Sbok) = 2.25 * S.

Answer: the surface area of ​​a regular octagonal prism will increase 2.25 times: S1 = 2.25 * S.

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