Answer:
420 cm²
Explanation:
You want the surface area of a regular hexagonal prism with side length 4 cm, apothem 3.5 cm, and height 14 cm.
Base area
The area of one base is given by ...
B = 1/2Pa
where P is the perimeter and 'a' is the apothem.
Lateral area
The lateral area is the sum of the areas of the rectangular faces. That sum is ...
LA = Ph
Total area
Then the total area of the two bases and the sides is ...
SA = 2B +LA = 2(1/2Pa) +Ph = P(a +h)
The perimeter is 6 times the side length, so is ...
P = 6(4 cm) = 24 cm
Then the total area is ...
SA = (24 cm)(3.5 cm +14 cm) = (24·17.5) cm² = 420 cm²
The surface area of the regular hexagonal prism is 420 cm².
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Additional comment
The length of the apothem is rounded in the given figure. If the actual value for a side length of 4 cm were used, the surface area would be closer to 419.14 cm².
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