Draw a pentagon, with the horizontal part at the bottom and the point at the top.
Draw a line from the middle of the bottom line to the center of the pentagon. This line represents the apothem.
Draw a line from the center of the pentagon to the right end of the bottom line You should have formed a right triangle inside the pentagon.
Note the size of the two angles at the base of the triangle. The right angle is, of course, 90 degrees. The inside angles of all regular pentagons are 108 degrees, so the bottom right angle of the triangle is one-half of 108 degrees, giving a result of 54 degrees.
Use trigonometry to find the length of the apothem using this formula: apothem = tan 54 * (length of side / 2). For example, if the length of each side of the pentagon is 6 inches, the apothem = tan 54 * 3. To find this answer in inches, enter 54 into a scientific calculator, press the "TAN" button, then multiply the result by three to get the length of the apothem in inches. In this example, the answer is 4.13 inches.