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The area of a polygon is the area that a polygon occupies. It can be regular or irregular. Some fundamental polygons are rectangles, triangles, pentagons, hexagons and squares. All these polygons have their different areas and the method of calculating the same is also different. For example, finding the area of a regular polygon is easy due to known and definite dimensions of the same. In this way, the area of a square can be determined easily if the length of one side is known as it has all the sides equal. Therefore, there is a difference in calculating the area between regular and irregular polygons.
What is the Area of a Polygon and perimeters?
The definitional aspect of the polygon in measuring its area is talking about the area enclosed by it. One of the major aspects of the polygon is that these are closed plane shapes. Therefore, the calculation of the area of a polygon can be done by measuring the space that is occupied by it in a two-dimensional plane. The unit of its area is always represented by the squares. Area of polygons and perimeters of the same are the measurable values that can be determined by calculating the length of sides of the polygons. There are some differences between these two which is essential to understanding the basic differences? From the definitional aspect, the perimeters of a polygon can be defined as the total length of the boundary of a polygon. It can be obtained by adding the length of all the sides. On the other hand, the area of a polygon can be defined as the space or region that the polygon enclosed. The formula of calculating the perimeters of the polygon can be stated as adding the length of side and side two and so on. That is perimeter = length of side 1+2+3+…..+N. On the other hand, the area of a polygon can be determined depending upon the polygon whether regular or irregular. In the case of unit measurement, the unit of perimeters of a polygon can be expressed by meter, cm, inches. The unit of area of a polygon is expressed by (meters)2, (inches)2 and so on. The only similarities between area and perimeters of polygon calculation are that both depend on the length of sides of shape ignoring the interior or exterior angles of the polygon.
Area of Polygon Formulas
There are two types of the polygon; regular and irregular. Therefore, there is a different set of calculating formulas for those regular and irregular polygons. Areas of some commonly known polygons are; area of triangle= base* height* (1/2). Along with this, the area of a parallelogram is base multiplied by the height of the same. That is, height * base. The area of a rectangle can be measured by multiplying its length with its width. That is, length* width. Apart from that, the area of trapezium can be calculated using the formula. That is, (some length of all the parallel sides or base) *(1/2) * height.
Regular polygons are those which have equal angles and sides. Some regular polygons and their formula have been described. The area of Equilateral triangles can be calculated by the formula where the square root of the length of the sides is multiplied by the root over 3 and the whole figure is then divided by 4 to get the result. That is = (√3 ×(length of a side)2)/4. Calculation of the area of a square is simple and can be obtained by the square root of the length of the sides. On the other hand, irregular polygons are the polygons on a plane closed shape which does not have equal sides or angles. Therefore, segregation of the irregular polygon is done and some regular shapes are calculated in the same irregular polygon to determine the area.
Area of Polygons with Coordinates
Various steps have to be adopted to find the area of a polygon with coordinates. In step one, one has to find the distance between all the points by adopting the distance formula. This distance formula is D which is equal to the square root of (X2-X1) added by the square of (Y2-Y2) where, X2, X1, Y2, Y1 are the points of distance. In step two, after the dimensions have been known, one has to find the polygon whether regular or irregular. In the third step, for a regular polygon use formula = (length of one side + number of sides + apothem)/2 where the length of apothem is calculated as (length of one side)/ (2 × (tan (180°/ number of sides))). In case the polygon is irregular, the whole polygon needs to be divided into several regular polygons to find the area of the same.
Conclusion
Therefore, it can be concluded that polygons have different aspects which should be taken into consideration before applying any formula for measuring the area of any polygon. There are differences between the perimeters of polygon and the area of the same which has been discussed above. The area of calculating the regular shape polygons is easy by applying some formulas. On the other hand, irregular polygons have to be calculated by measuring the sides of the regular nature of irregular polygons and at last adding all the outcomes. The coordinates based area measurement of the polygon is done by calculating the distance of all the points of the polygon.
