The area of a regular polygon can be found using the formula:
A =1/2ap
where a is the length of the apothem (the distance from the center of the polygon to the midpoint of a side), and
p is the perimeter of the polygon (the sum of the lengths of all its sides)
Another way to express this formula is:
A = 1/2nr^2 x sin2π/b
where
n is the number of sides of the polygon, and
r is the radius of the circle circumscribing the polygon
There are also specific formulas for finding the area of certain regular polygons. For example, the area of an equilateral triangle with side length
a
a is:
A = sqrt3/4 x a^2
The area of a square with side length
a is:
a = a^2
The area of a regular pentagon with side length
a is:
A = 5/4 x a^2 x (sqrt 1+2/sqrt5)
It's important to note that the formulas for finding the area of regular polygons assume that the polygon is regular, meaning that all of its sides and angles are congruent. If the polygon is not regular, the area must be calculated using a different method