Question

How do I find the area of a hexagon when the apothem is 2 times the square root of 3?

Answer 1

You know that we can create 6 equilateral triangles in a hexagon. An apothem is the height of each of these triangles. So with this I guess you can find the area of a triangle. So the area of the hexagon will be 6 times the area of a triangle

Answer 2

But how do I multiply 2 times the square root of 3, by the base of the triangle, (in this case 4), and get the same formatted answer (something times the square root of something)? I don't know if I'm making any sense...

Answer 3

All of the triangles in the figure below are congruent. What is the area of the figure? Note that all measurements are in centimeters.

Note that the apothem shown is equal to 2 times the square root of 3

Answer 4

I already have the area of all of the exterior triangles.. and I'm pretty sure that would equal the area of the hexagon.. but the answer choices they gave me don't make any sense to me

Answer 5

Actually I was refering to triangles like this

Answer 6

Yes, I've already done that. The height of one of the triangles would be 2 times the square root of 3, and the base would be 4. How do I multiply those two?

Answer 7

area of the triangle = 1/2 x height x base

just substitute

Answer 8

I don't know anything about numbers with square roots. :/ I don't know where to begin.

Answer 9

Ok,
let's take the equation
if area of the triangle is A,
$$A=\frac{1}{2}\times (2\times\sqrt{3})\times 4$$
you just have to keep the square root one aside and simplify what you can thus makes A,
$$A=\frac{1}{\not 2}\times (\not2\times \sqrt{3})\times 4=4\sqrt{3}$$

Answer 10

Ohhhh, okay. So the area of the triangle would be \[4\sqrt{3}\]? That's it? I'd hvae to multiply it by 6 thought, right?

Answer 11

Yep. The answer is there

Answer 12

Is it 24 to the square root of 3? :D

Answer 13

yes, you've got it right

Answer 14

Awesome! Thank you so much! (:

Answer 15

you're welcome :)