PLS HELP: Find the surface area of the regular hexagonal pyramid.

[EmmaVorne]

Find the surface area of the regular hexagonal pyramid. Round your answer to the nearest hundredth.

 

[HallsofIvy]

Since the base is a regular hexagon, each of the six triangles the base is divided into is an equilateral triangle. Each side of the base is equal to the length of the line from the center to the end of a side. And that means that the altitude shown divides the triangle into two "30- 60 right triangles". In particular, one leg of that right triangle (the one on the side of the hexagon) is half the length of the hypotenuse. If we call the side of the hexagon "s", the hypotenuse has length 2s and so , by the Pythagorean theorem, $\displaystyle s^2+ (2\sqrt{3})^2= (2s)^2$ or $\displaystyle 4s^2- s^2= 3s^2/4= 12$. Find "s" and you can find the area or all the triangles in the base and so the area of the base. Also, once you have s, you know the base of each of triangles in the upright portion and can use the Pythagorean theorem again to find the altitude of each triangle.

 

[mmm4444bot]

Hi Emma. Is this homework? Are you the student? Were you given lessons or a formula? What have you tried or thought about, thus far?

There is more than one formula, for the total surface area. I can't know what the class is doing, until you explain where you're stuck or show some work.

Here is one formula:

3*(base length)*(apothem + slant height)

They've given you the base length and the apothem; you may find the slant height by using the Pythagorean Theorem.

Does any of this look familiar to you? Do you have a specific question?

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