What radius of a circle is required to inscribe a regular hexagon with an area of 166.28 in2 and an apothem of 6.928 in?

If you want to inscribe a polygon inside a circle, you have a formula that doesn't have to use the apothem. The formula is:

A = (nr²/2)sin(360/n)

Since the polygon is a hexagon, it has 6 sides. Thus, n = 6. Knowing the area, we can determine the radius of the circle, r.

166.28 = (6r²/2)sin(360/6)
r = 8 inches

Thus, the radius of the circle is 8 inches.

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two  numbers we need to have  the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n.  n+5n=726n=72n=(72/6)n=12  now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60