What is the apothem of a pentagon with a side = 3cm?
The apothem of a pentagon is a segment with one endpoint at the center of the pentagon and the other at the midpoint of a side. If the pentagon is regular (it must be regular to work this problem), then you can divide the pentagon into five congruent triangles by connecting the center of the pentagon to each of the five vertices. Taking only one of these (isosceles) triangles, you can find the vertex angle by dividing 360 degrees by 5. So, the vertex of the triangle is 72 degrees. When you draw in your apothem, which is the altitude of the isosceles triangle from the vertex, then you will bisect the 72 degree angle producing two 36 degree angles… and you will bisect the side producing two segments of 1.5 cm. Finally, use trigonometry to set up an equation to find the length of the apothem. tan 36 = 1.5/a a = 1.5/(tan 36) The apothem is approx.
