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you want the surface area correct?

yes

|dw:1436465833356:dw|

Do you know how to find the area of the|dw:1436465959427:dw|??

no...

|dw:1436466095899:dw|

x²+6²=10²
x=?

4^2

I guess we should start over from when I split the triangle

|dw:1436466297750:dw|

can you find this missing side>?

64?

yes

the missing height is 8.

|dw:1436467003677:dw|

can you find the area of this triangle? (shaded) |dw:1436467035260:dw|

24?

yes

and the area of the whole triangle would be?

yes

What if I told you to find the area of this:|dw:1436467254378:dw|(our 4th face in a pyramid)

I will split this triangle in halves as well.

|dw:1436467297253:dw|

can you find the height using the pythegorian theorem a²+b²=c² ?

ok, you are missing the leg or the hypotenuse here?

Leg?

yes

please take a shot to plug in numbers into
a²+b²=c²
(if you make a mistake it is ok, i will correct)

\[a ^{2}+6^{2}=12^{2} ?\]
\[a ^{2}=108\]
\[a=6\sqrt{3}\]

yes.
a=√108
a=√(36•3)
a=6√3
correct

|dw:1436467977322:dw|

|dw:1436468071869:dw|

So your 4th face is 36√3.

\[144+36\sqrt{3}\]?

yes

Thank you!!