Question

what is the total surface area of the drawing?
a) 256 km²
b) 549 km²
c) 564 km²
d) 265 km²

Explanation:

Step1: Calculate the area of the two pentagonal bases

The formula for the area of a regular pentagon is \(A = \frac{5}{2} \times s\times a\), where \(s\) is the side length and \(a\) is the apothem. Here \(s = 9\) km and \(a=6.2\) km.

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Step2: Calculate the lateral surface area

The lateral surface area of a pentagonal prism is \(A_{lateral}=Perimeter\times height\). The perimeter of the pentagon \(P = 5\times9=45\) km and the height \(h = 6\) km.

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Step3: Calculate the total surface area

The total surface area \(A_{total}=A_{base}+A_{lateral}\)

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Answer:

B) \(549\space km^{2}\)