what is the area of a regular polygon with 13.8 area and 6 sides
It would help if you proofread your questions before you posted them.
13.8?
To find the area of a regular polygon, you can use the formula:
Area = 0.5 * apothem * perimeter
where:
- Apothem is the distance from the center of the polygon to any side (perpendicular distance).
- Perimeter is the total length of all sides of the polygon.
In this case, you are given the area (13.8) and the number of sides (6). We need to find the apothem and the perimeter to calculate the area.
To find the apothem, we can use the formula:
Apothem = (side length) / (2 * tan(180° / number of sides))
Since we are given the number of sides (6), we can substitute this into the formula and solve for the apothem.
Apothem = (side length) / (2 * tan(180° / 6))
Next, we need to find the perimeter. Since we know the number of sides (6) and assume they are all equal in length for a regular polygon, we can calculate the perimeter using the formula:
Perimeter = (side length) * (number of sides)
To find the side length, we can rearrange the formula:
(side length) = Perimeter / (number of sides)
Now, let's calculate the side length using the given number of sides (6) and the area (13.8):
First, find the perimeter:
Perimeter = (side length) * (number of sides)
Perimeter = (side length) * (6)
Next, find the side length:
(side length) = Perimeter / (number of sides)
(side length) = Perimeter / 6
Finally, substitute the known area (13.8) into the formula for area and solve for the apothem:
Area = 0.5 * (apothem) * (Perimeter)
13.8 = 0.5 * (apothem) * (Perimeter)
Now that we have the perimeter and side length, we can solve for the apothem:
Apothem = (side length) / (2 * tan(180° / 6))
Once we have the apothem and the perimeter, we can use the area formula to find the area of the regular polygon:
Area = 0.5 * (apothem) * (Perimeter)