Input Data :
Number of sides n = 5
Side length l = 10
Objective :
Find what is the interior angle, exterior angle, area & perimeter of the polygon?
Solution :
Interior Angle = (n - 2) x 180n
= (5 - 2) x 1805
= 3 x 1805
= 5405
Interior Angle = 108
Sum of Interior Angle = (n - 2) x 180
= (5 - 2) x 180
= (3) x 180
Sum of Interior Angle = 540
Exterior Angle = 360n
= 3605
Exterior Angle = 72
Perimeter = Side x Side Length
= 5 x 10
Perimeter = 50
Area = Side Length x (Perimeter/2)2 tan(180/n)
= 10 x (50/2)2 tan (180/5)
= 10 x 252 tan (36)
= 2502 x 0.7265
= 2501.4531
Area = 172.0477
Area and perimeter of polygon calculator uses two parameters, number of sides and side length of a regular polygon, and calculates the sum of interior angles, measures of interior and exterior angles, perimeter and area of the polygon.
It is an online Geometry tool requires number of sides and side length of a regular polygon. Using this polygon calculator, we will understand methods of how to find the sum of interior angles, measures of interior and exterior angles, perimeter and area of any regular polygon.
It is necessary to follow the next steps:
A closed figure bounded by line segments is the polygon. These segments are called its edges or sides, and the points where two sides meet are the polygon's vertices.
For instance, in the following table are given some well-known polygons:
3 | Triangle |
4 | Quadrilateral |
5 | Pentagon |
6 | Hexagon |
7 | Heptagon |
8 | Octagon |
9 | Nonagon |
10 | Decagon |
12 | Dodecagon |
n | n-gon |
Calculating areas and perimeters of regular polygons play an important role in almost all field of science and real life. A polyhedron is a solid whose surface consists of a number of polygonal faces. A polyhedron is regular if all its faces are congruent regular polygons and the same number of faces meet at every vertex. There are five convex regular polyhedra, known as the \underline{Platonic solids}: tetrahedron, cube, octahedron and dodecahedron, icosahedron. The surface area and volume of a regular polyhedron contain the formula for the area of regular polygon.
Practice Problem 1:
Find the area of regular dodecagon with lengths of sides and apothem of $14$ and $35$, respectively.
Practice Problem 2:
Find the number of sides and the measure of interior angles of a regular polygon if the measure of its exterior angle is $36^o$.
The polygon calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students (K-12 education) to understand the concept of perimeter and area of regular polygons. This concept can be of significance in geometry, to find the area and volume of some solids. Real life problems on regular polygons involving side length, measures of angles, apothem length, area, and perimeter are very common so these formulas can be of great the importance of solving.