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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))
What else can I help you with?
What is the perimeter of a regular seven-sided polygon?
It is the sum of its 7 equal sides.
What is a regular four-sided polygon?
A square is a regular four-sided polygon.
What is the perimeter of a polygon with the area of 7?
If you restrict yourself to integers, the perimeter of a four-sided polygon is 16.
Is a hexagon a regular polygon or not a regular polygon?
A 6 sided hexagon polygon can be regular or irregular.
What is the perimeter of a retangular nongon?
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.
What is the perimeter of a regular seven-sided polygon?
It is the sum of its 7 equal sides.
What is a regular four-sided polygon?
A square is a regular four-sided polygon.
How do you find the perimeter of a pentagon?
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.
What is a five-sided polygon?
A five-sided polygon is called a pentagon. A regular five-sided polygon is simply called a regular pentagon
What is the perimeter of a polygon with the area of 7?
If you restrict yourself to integers, the perimeter of a four-sided polygon is 16.
Is a hexagon a regular polygon or not a regular polygon?
A 6 sided hexagon polygon can be regular or irregular.
What is a regular 18 sided polygon?
The name of a 18 sided polygon is Octadecagon.
What is the perimeter of a retangular nongon?
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.
What is the difference between a regular 9 sided polygon and a 9 sided polygon?
A regular polygon has equal length sides while a polygon does not have to have equal sides.
What do you call a 24-sided polygon?
The constructed polygon name for a 24-sided regular polygon is an icosikaitetragon.
Is a 7 sided polygon regular?
If the seven sides are all the same length , then it is a regular polygon. A seven sided polygon is named a 'HEPTAGON'. If the seven sides are regular then it can be named as a ' Regular Heptagon'.
What is the regular polygon with 12 sides?
It is a regular 12 sided dodecagon polygon
