Question

Find the area of a regular hexagon with the given measurement.

6-inch radius

6 is the radius i need to find the sqrt! please help! i didnt understand what the other ppl were writing down please explain it clearly for me thankies <3

Answer 1

but ineed to put it in sqrt

Answer 2

Sorry...was wrong on first post.

Answer 3

Let me start again.

Answer 4

The area of the regular polygon is\[(1/2)nsa\]where n is the number of sides (6), s is the length of the sides, and a is the apothem.

Answer 5

Since the radius is 6, in a hexagon (and only a hexagon), the side is equal to the radius. So s=6

Answer 6

Now to find the apothem, we use the formula (again...only for a hexagon) that\[a=(1/2)s\sqrt{3}\]

Answer 7

So, since s=6,\[a=(1/2)(6)\sqrt{3}=3\sqrt{3}\]

Answer 8

Now you have all the pieces you need.

Answer 9

Now the reason these all work for for only a hexagon is that a hexagon is made up of 6 equilateral triangles. That's why the side and radius are the same.

Answer 10

The apothem formula deals with the nature of 30-60-90 triangles which happen with equilateral triangles...probably more than you need to know though so I won't go into it unless you are curious.

Answer 11

Find the formula, in terms of K, for the area of a regular octagon with apothem K and side of 10. do u know this cus i dnt

Answer 12

So bottom line. A=(1/2)nsa
n=6,
s=6,
a=3sqrt(3)

A=(1/2)(6)(6)(3sqrt{3})

Answer 13

Ok...for that one, use the same formula. A=(1/2)nsa.

Answer 14

In this case, n=8 (octagon), s=10 (given in problem), and a=K (given in problem).

A=(1/2)(8)(10)K=40K.

Answer 15

I would suggest you memorize A=(1/2)nsa because it is very useful for the problems you are doing.

Answer 16

In most cases (if not all) they will give you at least two of the values of n, s, and a. The problems should be nice enough that you can find the third with a little geometry.

Answer 17

Final answer to your first one, btw, is 54sqrt(3)