Short Answer 
To calculate the area of a regular polygon, start by identifying the polygon type and determining its apothem using the formula ( a = frac{s}{2 times tanleft(frac{pi}{n}right)} ). Then, apply the area formula ( A = frac{1}{2} times n times s times a ) using the number of sides, side length, and apothem to find the total area.
Step 1: Identify the Polygon Type
Begin by determining the type of polygon you are working with. Focus on whether it is a regular polygon, where all sides and angles are equal. This classification will guide you in the subsequent calculations. Regular polygons include shapes like the triangle, square, pentagon, and hexagon.
Step 2: Find the Apothem
Once you have the type of polygon, the next step is to calculate the apothem using the formula: a = frac{s}{2 times tanleft(frac{pi}{n}right)}, where s is the length of one side and n is the number of sides. The apothem is a crucial element as it helps in determining the area by serving as the height when calculating the polygon’s area.
Step 3: Calculate the Area
Finally, use the area formula for your regular polygon: A = frac{1}{2} times n times s times a. Here, you’ll plug in the values of the number of sides n, side length s, and the apothem a. This will provide you with the total area of the polygon, allowing for effective geometric analysis.