The prism below has two faces that are regular hexagons. Each hexagonal face has an area of \( 23 \mathrm{~cm}^{2} \).
What is the surface area of the prism?
Remember to give the correct units.
Answer
Step 4: Determine the surface area of the prism using the formula \(SA = 2A + 6sh\).
Step 1 ：Step 1: Calculate the apothem (\(a\)) of the hexagon from its area using the formula \(A = \dfrac{3 \times p \times a}{2} \), where \(A\) is the area and \(p\) is the perimeter.
Step 2 ：Step 2: Determine the length of each hexagonal face's side (\(s\)) using \(p = 6s\).
Step 3 ：Step 3: Calculate the height (\(h\)) of the prism using the Pythagorean theorem and one equilateral triangle made by cutting the hexagon into 12 equal parts.
Step 4 ：Step 4: Determine the surface area of the prism using the formula \(SA = 2A + 6sh\).
