Question

Select the correct answer.A business award is in the shape of a regular hexagonal pyramid. The height of the award is 95 millimeters and the base edge is 44 millimeters.What is the surface area of the pyramid to the nearest square millimeter?A. 13,511 mm²B.17,616 mm²C.10,060 mm²D. 18,541 mm²

Answer 1

`SA=18,541\text{ mm}^2`

Explanation:

The surface area of a regular hexagonal pyramid is represented by the following equation:

`\begin{gathered} SA=(3ab+3bs)\text{ square units} \\ where,\text{ } \\ a=\text{ apothem of the pyramid} \\ b=\text{ base} \\ s=\text{ slant height} \end{gathered}`

Therefore, if the height of the award is 95 millimeters and the base edge is 44 millimeters.

Since it is a regular hexagon, the apothem is formed by an equilateral triangle, therefore using the Pythagorean theorem:

`\begin{gathered} a=√(44^2-22^2) \\ a=22\sqrt{3\text{ }}mm \end{gathered}`

Now, for the slant height, use the Pythagorean theorem too using the apothem and the given height:

`\begin{gathered} \text{ slant height=}\sqrt{(22√(3))^2+95^2} \\ \text{ slant height=102.36 mm} \end{gathered}`

Now, solve the equation of the surface area:

`\begin{gathered} SA=(3ab+3bs) \\ SA=(3(22√(3))(44)+3(44)(102.36) \\ SA=18,541\text{ mm}^2 \end{gathered}`