Thye area of a regular hexagon is 38 cm^2. What is the area of a regular hexagon with sides 4 times as long?
To find the area of a regular hexagon, you can use the formula:
Area = (3 * √3 * s^2) / 2,
where s is the length of the side.
Given that the area of the original hexagon is 38 cm^2, we can use this information to find the length of the side of the original hexagon.
38 = (3 * √3 * s^2) / 2.
To solve for s, we can rearrange the equation:
s^2 = (2 * 38) / (3 * √3).
s^2 = 76 / (3 * √3).
Now, we can find the length of the side, s:
s = √(76 / (3 * √3)).
Now that we have the length of the side, we can find the length of the side for the scaled-up hexagon.
The new length of the side = 4 * s.
Now, we can calculate the area of the scaled-up hexagon using the formula:
Area = (3 * √3 * (4 * s)^2) / 2.
Area = (3 * √3 * 16 * s^2) / 2.
Area = 24 * √3 * s^2.
Since we already know the value for s (obtained earlier), we can substitute it in the formula to find the area of the scaled-up hexagon.