A regular hexagon is inscribed inside a circle. The circle has a radius of 12
units.
A: What is the approximate measure of the
apothem of the hexagon?
B: What is the approximate area of the hexagon?
Can someone help me?
A hexagon inscribed in a circle results in 6 equilateral triangles, each with sides of 12 units (the given radius)
Look at one of these. Isn't the apothem the height of one of those triangles ? See ...
https://en.wikipedia.org/wiki/Apothem
draw in the altitude, (apothem)
you an now use Pythagoras:
heigth^2 + 6^2 = 12^2
height^2 = 108
height = √108 = appr ......
you can now find the area of one of them, then multiply by 6 to get the whole hexagon.
Certainly! I can help you with that. To find the apothem of a regular hexagon inscribed inside a circle, you can use the formula:
apothem = radius * cos(30 degrees)
In this case, since the radius of the circle is given as 12 units, we can substitute that into the formula:
apothem = 12 * cos(30 degrees)
To find the value of cos(30 degrees), you can use a calculator or refer to a trigonometric table. The approximate value of cos(30 degrees) is √3/2.
So, the apothem of the hexagon is:
apothem = 12 * (√3/2)
To simplify this expression, multiply 12 by √3/2:
apothem ≈ 6√3 units.
Now let's move on to finding the approximate area of the hexagon. The formula for the area of a regular hexagon is:
area = (3√3 * side length^2) / 2
To find the side length, we can use the radius of the circle. Since the radius of the circle is 12 units, the side length of the hexagon is equal to the diameter of the circle, which is twice the radius:
side length = 2 * radius
substituting the given value:
side length = 2 * 12
side length = 24 units.
Now, we can calculate the area using the formula:
area = (3√3 * 24^2) / 2
Calculating this expression will give us the approximate area of the hexagon.
I hope this explanation helps you solve the problem! If you have any further questions, feel free to ask.