Question

Find the area of a regular pentagon with a side length of 14 and an apothem of 22.

Answer 1

well let me explain how do you find the Area of Regular Polygons and the apothem

Answer 2

the area 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. Apothem is the line segment from the center of a regular polygon to the midpoint of a side. Perimeter can be found by multiplying the side length with the number of sides in the polygon. 2
Along with the side length, if the length of the apothem is also directly given, then the finding the area of such a polygon is no more than a cake walk. Simply plug in the values of a and p in the formula and get the area. For example, consider finding the area of a regular hexagon (6 sides) of side length 10 units and apothem measuring 5sqrt(3) units.
3
Along with the side length, if the length of the apothem is not directly given then it can be calculated using the following formula:

a = (s/2) x cot(1800/n),

where a is the length of the apothem, s is the side length, and n is the number of sides in the polygon.

As an example, consider finding the area of a regular nonagon (9 sides) of side length 5 units.Find the apothem
Find the Area of Regular Polygons
Find the perimeter
Find the Area of Regular Polygons
Find the area using the formula mentioned in Step 1 above.