posted by Fustrated on .
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?
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.
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