Problem : Howm do you find the area of a circle circumscribed about a regular pentagon with a perimeter of 50 inches.

So far I each side of pentagon is 10. How do I find the radius of the circle? Is this the correct direction to go?
I your link & I was unable to come up with the correct answer of 227.3in^

To find the radius of the circle circumscribed about a regular pentagon, you can use the formula:

Radius = (Side Length / 2) * (1 / sin(π/5))

Given that each side of the pentagon is 10 inches, the radius can be calculated as follows:

Radius = (10 / 2) * (1 / sin(π/5))

To find the value of sin(π/5), you can use a calculator in radian mode. On most calculators, it is denoted by "sin^-1" or "arcsin".

Once you find the value of sin(π/5), substitute it into the formula to get the radius.

Finally, to find the area of the circle, you can use the formula:

Area = π * Radius^2

Plug in the calculated radius into this formula to find the area. Round the answer to the appropriate number of decimal places.

To find the radius of the circle circumscribed about a regular pentagon, you can use the following equation:

radius = (side length of pentagon) / (2 * sin(180°/number of sides))

In this case, since you mentioned that each side of the pentagon is 10 inches, we can substitute this value into the equation:

radius = 10 / (2 * sin(180°/5))

Simplifying further using trigonometric functions, we have:

radius = 10 / (2 * sin(36°))

Now, to find the value of sin(36°), you can use a scientific calculator or refer to a trigonometric table. Once you find the value of sin(36°), you can substitute it back into the equation to get the radius.

Using this calculated radius, you can then find the area of the circle using the formula:

area = π * (radius)^2

After calculating the area, you should get the correct answer of approximately 227.3 square inches.

Remember to use the correct units when expressing the answer (in this case, square inches).