Find the are of a regular 16-side polygon of side length 10cm
To find the area of a regular polygon with side length "s" and number of sides "n", we can use the formula:
Area = (n * s^2) / (4 * tan(π/n))
In this case, we have a regular 16-sided polygon with side length 10 cm. Plugging in the values:
n = 16 (number of sides)
s = 10 cm (side length)
Area = (16 * 10^2) / (4 * tan(π/16))
Area = (16 * 100) / (4 * tan(π/16))
Area = 1600 / (4 * tan(π/16))
Now, calculate the value of tan(π/16) which is approximately 0.1989:
Area = 1600 / (4 * 0.1989)
Area = 1600 / 0.7956
Area ≈ 2010.0451 cm^2
Therefore, the area of a regular 16-sided polygon with side length 10 cm is approximately 2010.0451 square centimeters.