Question 1032156
the polygon has 18 sides.
the central angle is therefore equal to 360 / 18 = 20 degrees.
the polygon is divided into 18 isosceles triangles whose vertex is equal to 20 degrees and whose altitude (the apothem) is equal to 3.
each of these isosceles triangle is divided into two equal right triangles with their central angles equal to 10 degrees.
solve for the base of each of these right triangle by using the tangent formula.
you get tan(10) = x/3, where x is the base and 3 is the altitude.
solve for x to get x = 3 * tan(10).
since the base of the isosceles triangle is 2x, then you get 2x = 6 * tan910).
the area of each of the isosceles triangl;e is equal to 1/2 * base * height.
this becomes 1/2 * 6 * tan(10) * 3 which results in the area of one of the isosceles triangles is equal to 1.586942826 square units.
since there are 18 of these isosceles triangles in the polygon, then multiply this by 18 to get area of the polygon with 18 sides is equal to 28.56497087 square units.
you can round this to as many desimal digits as required.
if 2, then 28.56
if 3, then 28.565
if 4, then 28.5650
if 5, then 28.56497
etc.,
this is what your polygon looks like:
<a href = "https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Regular_polygon_18_annotated.svg/220px-Regular_polygon_18_annotated.svg.png" target = "_blank">https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Regular_polygon_18_annotated.svg/220px-Regular_polygon_18_annotated.svg.png</a>
each of those little triangle with a vertex angle of 20 degrees is an isosceles triangle.
the apothem is the altitude of each of them.