Question

a regular hexagonal prism with a height of 25 cm has side lengths of 5 cm and a base area of 65 cm². what is the surface area of the prism? 750 cm² 1,625 cm² 815 cm² 880 cm²

Explanation:

Step1: Find the lateral surface area

A regular hexagonal prism has 6 rectangular lateral faces. The formula for the lateral surface area \(LSA\) of a prism is \(LSA = perimeter\times height\). The perimeter \(P\) of the base (a regular hexagon) with side length \(s = 5\) cm is \(P=6s\). So \(P = 6\times5=30\) cm. The height \(h = 25\) cm. Then \(LSA=30\times25 = 750\) \(cm^{2}\).

Step2: Find the total surface area

The formula for the total surface area \(TSA\) of a prism is \(TSA=2\times(\text{base area})+\text{lateral surface area}\). Given the base area \(B = 65\) \(cm^{2}\). Then \(TSA=2\times65+750\). First, calculate \(2\times65 = 130\). Then \(TSA=130 + 750=880\) \(cm^{2}\).

Answer:

\(880\ cm^{2}\)