Learn how to calculate the area of a polygon given below with our step-by-step guide. Discover the formula and definition of polygons here.

Introduction

Calculating the area of a polygon is an essential concept in mathematics, engineering, and architecture. The measurement of the polygon’s area helps determine the surface area of various objects, including buildings, bridges, and other structures. However, the calculation of the polygon’s area can be a daunting task, especially for beginners in mathematics. In this article, we will explain what a polygon is, the formula for calculating its area, and how to compute the area of a polygon given below.

Definition of Polygon

A polygon is a two-dimensional plane figure consisting of straight lines that form a closed shape. The most common types of polygons are triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons. The sides of a polygon are called edges, while the corners are referred to as vertices. Polygons can be regular or irregular, convex or concave, depending on their shape and angles.

A regular polygon is a polygon that has equal angles and sides. On the other hand, an irregular polygon has sides and angles of different lengths and measures. Convex polygons have all their interior angles less than 180 degrees, while concave polygons have at least one interior angle greater than 180 degrees.

Formula for Calculating Area of a Polygon

The formula for calculating the area of a polygon depends on the type of polygon and the available information. To find the area of a regular polygon, we can use the formula:

Area = (1/2) * perimeter * apothem

Where the perimeter is the total length of the polygon’s sides, and the apothem is the distance from the polygon’s center to the midpoint of any side.

For an irregular polygon, we can divide it into triangles and calculate the area of each triangle using the formula:

Area = (1/2) * base * height

Then, we can sum up the areas of all the triangles to get the total area of the polygon.

Description of Given Polygon

Let’s consider the polygon shown below:

This polygon is an irregular hexagon with six sides and six vertices. The given lengths of the sides are 4 cm, 5 cm, 6 cm, 7 cm, 8 cm, and 9 cm. To calculate the area of this polygon, we need to divide it into triangles and find the area of each triangle using the formula mentioned above.

Steps to Calculate Area of Given Polygon

To calculate the area of a polygon, we need to use the formula that applies to the specific polygon type. In the case of the polygon given below, which is a regular hexagon, we can use the formula:

Area = 3√3/2 × s²

Where s is the length of the hexagon’s side.

To find the area of the given polygon, we need to know the length of one of its sides. Suppose the length of the side is 8 cm. We can substitute this into the formula and get:

Area = 3√3/2 × 8²
Area = 3√3/2 × 64
Area = 3√3 × 32
Area = 55.425 cm² (rounded to three decimal places)

Therefore, the area of the given polygon is 55.425 cm².

Conclusion

Calculating the area of a polygon is an essential skill in mathematics and other fields that require geometric calculations. By following the steps outlined in this article, you can easily calculate the area of a regular hexagon or any other polygon type. Remember to use the appropriate formula and units of measurement to get accurate results. With practice, you can become proficient in calculating the area of any polygon, no matter how complex it appears.