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 3 square root of three.

Question

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 3 square root of three.

anonymous · Answer

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0701_06/image0024e7204bc_a.gif

hero · Answer

The sides equal 4 and the base equals 6. Also, you can split the hexagon in the center into triangles as well:

anonymous · Answer

okay...

hero · Answer

Now all you have to do is use Heron's formula to find the area of one of the triangles, then multiply that by the total number of triangles, 12.

anonymous · Answer

what in the world is Heron's Formula?

hero · Answer

$A = \large\sqrt{s(s-a)(s-b)(s-c)}$

$\huge s = \frac{a + b + c}{2}$

a, b, c are sides of the triangle

hero · Answer

A = area of the triangle

hero · Answer

In this case, a = 4, b = 4, c = 6

anonymous · Answer

the only thing even close to that I learned is A=1/2bh

hero · Answer

What I showed you is an alternate formula for use when you know the lengths of the sides

anonymous · Answer

so what do I do?

hero · Answer

Solve it using the information I gave you.

hero · Answer

You have the values of a, b, and c. Now, calculate s and use the new formula for Area.