The polygon will consist of 24 congruent isosceles triangle each having 2 equal angles of 82.5 degrees and 2 equal sides of 19.15324394 cm with an apex angle of 15 degrees opposite the base of 5 cm.
Area of triangle: 0.5*19.15324394^2 *sin(15)*24 = 1139.363 square cm to three decimal places
If you restrict yourself to integers, the perimeter of a four-sided polygon is 16.
Perimeter = 2*Area/Apothem.
Find the apothem of a regular polygon with an area of 625 m2 and a perimeter of 100 m.
12Infinitely many all different:As it is only the area that matters, the perimeter can be any shape:An equilateral triangle (with sides approx 3.398 units)A square (with sides approx 2.236 units)A regular pentagon (with sides approx 1.705 units)A regular hexagon (with sides approx 1.387 units)A regular heptagonA regular octagonA regular nonagonA regular decagonA regular hendecagon (11 sided polygon)A regular dodecagon (12 sided polygon)A regular triskaidecagon (13 sided polygon)A regular 14 sided polygonA regular 15 sided polygonA regular 16 sided polygon...A circle (with radius approx 1.262 units)And there are also the non-regular shapes, eg an L shaped hexagon, a kite, a parallelogram which can have an area of 5 square units.
Unless the area is a regular polygon (or a circle) you cannot.
If you restrict yourself to integers, the perimeter of a four-sided polygon is 16.
Area of regular polygon: 0.5*apothem*perimeter
Perimeter = 2*Area/Apothem.
Find the apothem of a regular polygon with an area of 625 m2 and a perimeter of 100 m.
12Infinitely many all different:As it is only the area that matters, the perimeter can be any shape:An equilateral triangle (with sides approx 3.398 units)A square (with sides approx 2.236 units)A regular pentagon (with sides approx 1.705 units)A regular hexagon (with sides approx 1.387 units)A regular heptagonA regular octagonA regular nonagonA regular decagonA regular hendecagon (11 sided polygon)A regular dodecagon (12 sided polygon)A regular triskaidecagon (13 sided polygon)A regular 14 sided polygonA regular 15 sided polygonA regular 16 sided polygon...A circle (with radius approx 1.262 units)And there are also the non-regular shapes, eg an L shaped hexagon, a kite, a parallelogram which can have an area of 5 square units.
A = (1/2)Pa A being the area, P being the perimeter of the regular polygon, and the apothem length being a.
Unless the area is a regular polygon (or a circle) you cannot.
The formula used to find the area of any regular polygon is A = 1/2 a P where the lower case a stands for the length of the apothem and the uppercase P stands for the perimeter of the polygon.
Such a polygon is not possible.
The area of a regular polygon is equal to (1/2)pa, where p is the perimeter and a is the apothegm. The area of this polygon is (1/2)(15.44)(16), which is 123.52 square units.
Area of regular polygon: 0.5*3*20 = 30 square feet
The area of a polygon is not enough to determine its shape - unless it is a regular polygon. There is nothing in the question to suggest that the octagon is regular.