How would I calculate the perimeter of a hexagon (which can be divided into 6 congruent equilateral triangles) which is inside a circle with an area of 314^2 cm?
Many thanks
To calculate the perimeter of a hexagon inside a circle, we need to first find the length of one side of the hexagon. We know that the hexagon can be divided into 6 congruent equilateral triangles.
The formula to find the area of an equilateral triangle is A = (sqrt(3)/4) * s^2, where A is the area and s is the length of one side of the triangle.
Since the hexagon is made up of 6 equilateral triangles, the total area of the hexagon is 6 times the area of one equilateral triangle.
Given that the area of the circle is 314^2 cm, we can find the radius of the circle using the formula A = π * r^2, where A is the area and r is the radius.
Plugging in the values, we get:
314^2 = π * r^2
Now, solve the equation for r:
r^2 = 314^2 / π
r^2 = 314^2 / 3.14
r^2 ≈ 99996.8153
r ≈ sqrt(99996.8153)
r ≈ 316.22 (rounded to two decimal places)
Since the hexagon is inscribed in the circle, the length of one side of the hexagon is equal to the radius of the circle, which is approximately 316.22 cm.
Now, to find the perimeter of the hexagon, we multiply the length of one side by 6, since a hexagon has 6 sides.
Perimeter of hexagon = 316.22 cm * 6
Perimeter of hexagon ≈ 1897.32 cm
Therefore, the perimeter of the hexagon inside a circle with an area of 314^2 cm is approximately 1897.32 cm.