How do you find an apothem for a regular pentagon?

Question

How do you find an apothem for a regular pentagon?

Answer 1

To find the apothem, the problem will usually give you the length of all the sides around. and the slant height of the pentagon to the center. You can make a triangle using the length of the side and the slant height. Then turn it into a right triangle and use a^2+b^2=c^2

Answer 2

Depends on what you know about it.  In general, make a sketch of the pentagon.  Drop and apothem and a radius from the center.  Note that you've created a right triangle with the apothem as one of the legs.  You should be able to figure out the size of the interior angles of a pentagon, and the radius you drew will bisect one of those angles, so you'll know the size of the angle opposite the apothem.  The apothem will also bisect one side.  So:  if you know the radius, you can use the sine of the angle you know to get the apothem.  If you know the length of a side, you can use the tangent of that angle.

Edit:  The segment from the center to a vertex is called the radius.  The term "slant height" applies to solids, and has nothing to do with the center of a regular polygon.