How to find the surface area of a pyramid which has a regular hexagonal base of edge 6 cm and a height of 8 cm?

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- Dec 4th 2007, 11:43 PMkapitanvickiFind SURFACE AREA of a pyramid (hexagonal-base)?
How to find the surface area of a pyramid which has a regular hexagonal base of edge 6 cm and a height of 8 cm?

- Dec 5th 2007, 12:26 AMTwistedOne151Surface area
The area of the base should be simple, so the problem is the six triangular sides. Each triangle has area , where b = 6 cm is the length of a side of the base, and l is the height of the triangle. Consider the right triangle formed by a line from the center of the base to the center of one of the sides of the base, by the center axis of the pyramid, and the height l of the side in question. Since b=6 cm, the distance from center of base to the side of the base is . Thus by the pythagorean theorem, , and . From here, you can find the area of one of the triangles. Then just multiply by 6 to get the entire lateral area, and add the area of the base for the entire surface area.

--Kevin C. - Dec 5th 2007, 12:31 AMDivideBy0
For the base (img1):

You can divide it up into 6 equilateral triangles by drawing diagonals from opposite points.

The area of each of the equilateral triangles is

So the Total Base Area is

Now for the slanting plane areas (img2):

From before, we learnt that the length of is

Also, , as given.

Therefore, can be found by Pythagoras:

is the height of the triangular plane, so we can now work out its area:

Multiplying by 6 gives us the area of all of them =

So the total surface area is - Dec 5th 2007, 02:17 AMkapitanvicki
Thank you, divideby0! excellent answer (dont have much of an aptitude for maths) hehe...