## What formulas are used to find the area of a polygon?

The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].

**How do you find the perimeter and area of a polygon?**

The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and p is the perimeter of the polygon. Plug the values of a and p in the formula and get the area. As an example, let’s use a hexagon (6 sides) with a side (s) length of 10.

**What is the formula of irregular shape?**

Area of the given irregular shape = Area of the rectangle ‘P’ + Area of the semicircle ‘Q’ + Area of the triangle ‘R’ + Area of the rectangle ‘S’. ⇒ Area of the given irregular shape = 48 + 39.25 + 24 + 48 = 159.25 square units. Therefore, the area of the given irregular shape is 159.25 square units.

### Does Heron’s formula work for polygons?

Yes there is such a formula: Heron’s Formula. Heron’s formula allows you to calculate the area of a triangle if you know the lengths of all the sides of the triangle. With the information you have, you can divide the polygon into triangles whose side lengths you can calculate.

**What is a polygon in math?**

A polygon is any closed figure with all line-segment sides. So here we have an example of a polygon with three sides, a triangle with four sides, a quadrilateral and then one with five sides and six sides. And you could imagine, you could have many, many more sides. A geometric figure is not a polygon if first of all, the figure doesn’t close.

**How do you know if a geometric figure is a polygon?**

A geometric figure is not a polygon if first of all, the figure doesn’t close. So for example, something like this, not a polygon, has none of the polygon properties.

#### What is an equiangular polygon?

A closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex. Regular – all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral. Equiangular – all angles are equal.

**What is the sum of the angles in a polygon?**

Angles in polygons. Of course, the sum of the three angles in a triangle is 180 degrees. The sum of the four angles in a quadrilateral is 360 degrees because we can divide a quadrilateral into two triangles along a diagonal. We can extend this pattern to higher polygons.