Answer:
Calculating the area of a polygon can be as simple as finding the area of a regular triangle or as complicated as finding the area of an irregular eleven-sided shape. If you want to know how to find the area of a variety of polygons, just follow these steps.
Step-by-step explanation:
1.) Write down the formula for finding the area of a regular polygon. To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem.[1] Here is what it means:
Perimeter = the sum of the lengths of all the sides
Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side
2.) Find the apothem of the polygon. If you're using the apothem method, then the apothem will be provided for you. Let's say you're working with a hexagon that has an apothem with a length of 10√3.
3.) Find the perimeter of the polygon. If the perimeter is provided for you, then you're nearly done, but it's likely that you have a bit more work to do. If the apothem is provided for you and you know that you're working with a regular polygon, then you can use it to find the perimeter. Here's how you do it:
Think of the apothem as being the "x√3" side of a 30-60-90 triangle. You can think of it this way because the hexagon is made up of six equilateral triangles. The apothem cuts one of them in half, creating a triangle with 30-60-90 degree angles.
You know that the side across from the 60 degree angle has length = x√3, the side across from the 30 degree angle has length = x, and the side across from the 90 degree angle has length = 2x. If 10√3 represents "x√3," then you can see that x = 10.
You know that x = half the length of the bottom side of the triangle. Double it to get the full length. The bottom side of the triangle is 20 units long. There are six of these sides to the hexagon, so multiply 20 x 6 to get 120, the perimeter of the hexagon.
4.) Plug the apothem and the perimeter into the formula. If you're using the formula area = 1/2 x perimeter x apothem, then you can plug in 120 for the perimeter and 10√3 for the apothem. Here is what it will look like:
area = 1/2 x 120 x 10√3
area = 60 x 10√3
area = 600√3
5.) Simplify your answer. You may need to state your answer in decimal instead of square root form. Just use your calculator to find the closest value for √3 and multiply it by 600. √3 x 600 = 1,039.2. This is your final answer.
(Source: https://www.wikihow.com/Calculate-the-Area-of-a-Polygon)
