Question

Use the diagram of the regular pentagon to support an explanation showing why the formula

accurately yields the area of the pentagon. (Recall that a is the apothem and P is the perimeter of the

pentagon.)

A=1/2ap

Answer 1

@Chiko_1278

Answer 2

If you divide up the hexagon into six congruent triangles and add up the areas of each triangle, then you will see that the formula makes sense.

One-half the base of one of the six triangles times the apothem gives the area of one triangle. Adding this up six times, gives a/2( base + base + base + base + base + base). But the sum of the bases is the perimeter. So the area of the hexagon must be (a/2)(P)

Answer 3

It's not a hexagon though.....

Answer 4

would it still work?

Answer 5

hmm.. i think so