What is the area of a regular polygon with 16 sides and side length 4 inches

For a better understanding of the solution please find the diagram in the attached file.

The diagram is that of a triangular part of the regular polygon. The triangle is an isosceles triangle because the sides OA and OB are equal. Now, The angle . This is because the angle around the central angle of a polygon is 360 degrees in total.

Now, because is an isosceles triangle, angle OAP will be half of angle OAB. Thus, .

AP will be half of AB. Therefore, AP=2.

Now, the apothem, OP can thus be found as:

Thus the area of one triangle is

Therefore, the area of all the 16 triangles that make up the regular polygon is:

Thus the area of the polygon is 323.2 squared inches.

answer:      

step-by-step explanation: