Find the area of a regular 14-sided polygon given the side length is 21 centimeters. Give the answer to two decimal places.
First, we need to remember how we find the area of a regular 𝑛-sided polygon. The area will be equal to 𝑛 times 𝑥 squared over four times the cot of 180 over 𝑛, where 𝑥 equals the side length. And we should note here that we are operating with a cotangent in degrees. If the area equals 𝑛 times 𝑥 squared over four times the cot of 180 over 𝑛, since we know our figure is a 14-sided regular polygon, 𝑛 equals 14. And since our figure has a side length of 21 centimeters, 𝑥 equals 21, which means we have the area equals 14 times 21 squared over four times the cot of 180 divided by 14. 14 times 21 squared divided by four is 1543.5. We wanna multiply that by the cot of 180 divided by 14, which will be the cot of 90 over seven.
Don’t forget before you plug in the cot of 90 over seven to make sure your calculator or computer is set to degrees and not to radians. When you do that, you should get 4.38128 continuing, and then we’ll multiply that value by 1543.5, which gives us 6762.5153 continuing. If we want to round to two decimal places, we’ll consider the digit to the right of that and then round our area up to 6762.52. But what should the units be? We were given our side length in centimeters, which will make the area centimeters squared.