Join all vertices to the midpoint of the 15-agon. This will form 15 congruent isosceles triangles with an angle of 360° ÷ 15 = 24° at the centre and a base of length equal to that of the 15-agon = 360cm ÷ 15 = 24 cm
The area of the 15-agon is the sum of the areas of these triangles = 15 × area one triangle
Drop a perpendicular form the centre of the 15-agon to one side and it divides the isosceles triangle into two right angle triangles with an angle half that of the isosceles triangle at the centre of the 15-agon with one leg the height of the triangle and the other leg equal to half the side of the 15-agon
Using Trigonometry, the height of the triangle, and thus its area, and hence the area of the 15-agon, can be found.
height = ½ side / tan ½ angle at centre
→ area 15-agon = 15 × ½ × side × ½ side / tan ½ angle
= 15 × ¼ × side² ÷ tan ½ angle
= 15/4 × (24 cm)² ÷ tan(½×360°÷15)
≈ 10162 cm²
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Using the above it can be seen for a regular n-agon, the area is given by:
area = n × side² ÷ (4 × tan(180° ÷ n))
= perimeter² ÷ (4 × n × tan(180° ÷ n))
It is the sum of its 7 equal sides.
A square is a regular four-sided polygon.
If you restrict yourself to integers, the perimeter of a four-sided polygon is 16.
A 6 sided hexagon polygon can be regular or irregular.
I think you mean a regular nonagon. This is a nine-sided polygon. If you have the length of one side, you can multiply it by 9 to find the perimeter of all sides.
It is the sum of its 7 equal sides.
A pentagon, which is a 5-sided figure, will have a perimeter equal to the sum of the lengths of all the sides. This will be true for any polygon; the perimeter of any polygon is the sum of the lengths of all the sides. If the pentagon is a regular pentagon, then the perimeter will be 5 times the length of one of the sides. For any regular polygon, the perimeter will be the length of one side times the number of sides in that polygon.
A square is a regular four-sided polygon.
A five-sided polygon is called a pentagon. A regular five-sided polygon is simply called a regular pentagon
If you restrict yourself to integers, the perimeter of a four-sided polygon is 16.
A 6 sided hexagon polygon can be regular or irregular.
I think you mean a regular nonagon. This is a nine-sided polygon. If you have the length of one side, you can multiply it by 9 to find the perimeter of all sides.
The name of a 18 sided polygon is Octadecagon.
A regular polygon has equal length sides while a polygon does not have to have equal sides.
The constructed polygon name for a 24-sided regular polygon is an icosikaitetragon.
It is a regular 12 sided dodecagon polygon
A sixteen-sided regular polygon is called a hexadecagon or a hexakaidecagon.