How do calculate the length of the side of each polygon, when it does not have to be an integer value , and you are only allowed to investigate polygons with 3;4;6;8 and 12
To calculate the length of the side of a polygon, you need to use different formulas depending on the type of polygon you are dealing with. Here are the formulas for calculating the side length of polygons with 3, 4, 6, 8, and 12 sides:
1. Triangle (3 sides):
- Since the sum of all angles in a triangle is 180 degrees, we can use the Law of Cosines to find the side length:
- a^2 = b^2 + c^2 - 2bc * cos(A), where A is the angle opposite side a.
2. Quadrilateral (4 sides):
- For a general quadrilateral, there is no simple formula that can be applied to find the side length. However, if you have additional information about the quadrilateral, such as a right angle or symmetry, you can use trigonometric properties or other geometric methods to calculate the side length.
3. Hexagon (6 sides):
- Since all angles in a regular hexagon are equal to 120 degrees, and all sides are congruent, you can use the formula:
- S = P / 6, where S is the side length and P is the perimeter.
4. Octagon (8 sides):
- For a regular octagon, where all sides and angles are congruent, you can use the formula:
- S = P / 8, where S is the side length and P is the perimeter.
5. Dodecagon (12 sides):
- Similar to the hexagon and octagon, for a regular dodecagon, you can use the formula:
- S = P / 12, where S is the side length and P is the perimeter.
Note: When the side length of a polygon is not an integer value, you can represent it using decimals or fractions to get a precise measurement.
Remember, these formulas are just guidelines for finding the side length of each polygon. The exact method may vary based on the specific characteristics and information given for each polygon.