Question

A regular hexagon has sides of 3 feet. What is the area of the hexagon?

https://media.glynlyon.com/g_geo_2012/13/img_geou13a_64.gif

- 27 square root 3 ft2
- 18 square root 3 ft2
- 9 square root 3 ft2
- 13.5 square root 3 ft2

Answer 1

darn >.< can u attach :P

Answer 2

$$
A=\dfrac{3\sqrt 3}{2}h
$$
Where h is one side of your hexagon.

Answer 3

Correction:
$$
A=\dfrac{3\sqrt 3}{2}h^2
$$

Answer 4

then would it be
A= 3square root 3 over 2 times 3?

Answer 5

You got it.
but times 3 squared - my bad -- see correction

Answer 6

So 13.5 root 3 square feet

Answer 7

@ybarrap thank you! mind helping with another problem??

Answer 8

yw, okay

Answer 9

What is the length of DB ?
https://media.glynlyon.com/g_geo_2012/13/img_geou13a_49.gif

2
\[2\sqrt{3}\]
\[\sqrt{3}\]
1.5

Answer 10

The large right triangle is similar to the two smaller right triangles

DC is 6 sin 30 = 6 (1/2) = 3

We know because of similarity that Angle at vertex B is 60 degrees

So 3/DB = tan 60 or DB = 3/tan 60

That's it!

Can you determine DB now?

Answer 11

sin 60 = \( \dfrac{\sqrt 3}{2}\)
cos 60 = \( \dfrac{1}{2}\)
So, \(\tan 60 = \sin 60/\cos 60= \sqrt 3\)

Which means DB = \( \dfrac{3}{\sqrt 3}=\sqrt 3\).

Any questions?

Answer 12

no no i got it! thank you so much for all the explaining!

Answer 13

yw