Posted by **Fustrated** on Monday, February 6, 2012 at 9:40pm.

The base of a regular pyramid is a hexagon whose sides have length 5 ft. If a lateral edge of this pyramid has length 9 ft, what is the surface area of the pyramid?

- Geometry -
**drwls**, Monday, February 6, 2012 at 10:32pm
The distance from the apex to the middle of a side of the base is

sqrt(9^2 - 2.5^2) = 8.6458 ft

That equals the height h of one of the six triangular sides.

The area of one triangular side is

(1/2)*b*h = 21.615 ft^2

Multiply that by 6 for the total side area: 129.7 ft^2

You did not say if they wanted the area of the base included. That is easy enough to do.

- Geometry -
**Reiny**, Monday, February 6, 2012 at 10:33pm
You should be able to do the side triangles the same way I showed you in your other post.

The problem is the base.

It is a hexagon.

It is made up of 6 equilateral triangles.

For each triangle all sides are equal and all angles are 60°

Work on only one triangle

You can find the height by Pythagoras or simple trig

Then find the area of ONE triangle, then multiply by 6

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