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I feel your pain! 

Yessss!!    12 sqrt(3) !

12sqrt3?

Thank you, sorry I'm super ignorant here but, what would that calculation look like?

Area = 20.78  cm^2

If you need an answer with radicals in it (an EXACT solution)   , you will need to use

tan30 = 1/sqrt3     and tan60 = sqrt(3)  in the calculations to get the final answer

Thanks so much Pavlov!  Just to confirm, the total area is 20.78, right?  Or is 1/sqrt3 more accurate...

Note:  Units should be cm^2  (got cut off in scan)

(if you need EXACT values use  tan30 = 1/sqrt3    tan60=sqrt3  )

The surface area for a square pyramid is given by

Area = a^2 + 2a sqrt (( a^2)/4 +h^2)        (No, I didn't know that...I looked it up)

We have    a = 20   we just need to find h

tan (55) = h/10     h= 14.2814

Area = 20^2 + 2(20) sqrt (  400/4  + 7.14^2)  =1097.38 cm^2

For this problem you can use GERMDAS or PEMDAS.  These are acronyms to help you remember the order of operations.  GERMDAS stands for

Groupings

Exponents

Radicals

Multiplication

Division

Addition

Subtraction

So, to do this problem we have 

(1+1)x5x4

2x5x4

10x4

[40.]

Hope that helps!

The equation for the volume of a sphere

v = 4/3 pi r^3     r= radius = 1/2 diameter

  = 4/3 (3.14) (10^3) 

= 4186.67 in^3