A polygon is a two-dimensional shape made up of multiple straight sides that are connected at their endpoints. It can be regular, with all sides and angles of equal measure, or irregular, with sides of different lengths and angles. Whatever the shape, understanding how to calculate the area of a polygon is an important skill. This article will take you through the steps of finding the area of a polygon, no matter what shape it is.
Step 1: Identify the Number of Sides
The first step to finding the area of a polygon is to determine how many sides it has. If a polygon has four sides, it is known as a quadrilateral. If a polygon has five sides, it is known as a pentagon. If a polygon has six sides, it is known as a hexagon. The number of sides in a polygon can be determined by counting the number of straight lines that make up the shape.
Step 2: Measure the Length of Each Side
Once you have identified the number of sides in the polygon, the next step is to measure the length of each side. This can be done with a ruler or tape measure. Make sure to measure each side to the nearest whole number for accuracy. If there is a curved side, you will need to estimate the length of the side by measuring the diameter and dividing it by two.
Step 3: Calculate the Perimeter
Once you have the measurements of all the sides, the next step is to calculate the perimeter. The perimeter is the sum of all the side lengths. For example, if the side lengths of the polygon are 4 cm, 5 cm, 6 cm, and 7 cm, the perimeter is 4 + 5 + 6 + 7 = 22 cm.
Step 4: Determine the Apothem
The apothem is a line from the center of the polygon to the midpoint of any one side. To calculate the apothem, you need to know the length of one side and the interior angle of the polygon. The interior angle is the angle between two consecutive sides. For a regular polygon, all of the interior angles are equal. For an irregular polygon, the interior angles will be different. Once you know the length of one side and the interior angle, you can use the formula a = s/2tan(180/n) to calculate the apothem, where a is the apothem, s is the side length, and n is the number of sides.
Step 5: Calculate the Area
Once you have determined the perimeter and apothem of the polygon, you can use the formula A = (p x a)/2 to calculate the area. In this formula, A is the area, p is the perimeter, and a is the apothem. For example, if the perimeter is 20 cm and the apothem is 8 cm, the area of the polygon is (20 x 8)/2 = 80 cm.2
Step 6: Round the Answer
Once you have calculated the area, the last step is to round the answer to the nearest whole number. This is done by looking at the decimal place after the number. If the decimal place is 0.5 or higher, the number should be rounded up. If the decimal place is lower than 0.5, the number should be rounded down. For example, if the area of the polygon is 80.45 cm2, it should be rounded up to 81 cm2.
Conclusion
Finding the area of a polygon can be a tricky task, but with the right tools and knowledge, it is possible to calculate the area of any polygon, no matter what shape it is. By following the steps outlined in this article, you will be able to calculate the area of a polygon with ease.
