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Falling_In_Katt
 one year ago
Find the total area for the regular pyramid.
T. A. = \[([][][]+[][]\sqrt{[]})\]
Falling_In_Katt
 one year ago
Find the total area for the regular pyramid. T. A. = \[([][][]+[][]\sqrt{[]})\]

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2you want the surface area correct?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436465833356:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2Do you know how to find the area of thedw:1436465959427:dw??

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436466095899:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2I guess we should start over from when I split the triangle

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436466297750:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2now, you can almost find the area of this small triangle (and then multiply times 2 to get the area of the full triangle), BUT you don't know the hieght.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2U can see that the small triangle (formed by splitting the original triangle in halves) is a right triangle, and therefore we can apply a pythegorean theorem (a²+b²=c²) to find the missing height. in this case (as regards to this smaller triangle) we know a leg of 6 units a hypotenuse of 10. Therefore we will set the equation: a² + 6² = 10² (to solve for this missing height (or this missing leg)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2can you find this missing side>?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2a² + 6² = 10² a² + 36 = 100 a² = 64 good, but that is a² (you found that if you raise this missing side to the second power, then you get 64, BUT, you haven't found the actual side) Take the square root of both sides to find what "a" is going to be.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2the missing height is 8.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436467003677:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2can you find the area of this triangle? (shaded) dw:1436467035260:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2and the area of the whole triangle would be?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2(if a triangle with an area of 24 is only a half of the entire triangle, then the entire triangle is?)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2What if I told you to find the area of this:dw:1436467254378:dw(our 4th face in a pyramid)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2I will split this triangle in halves as well.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436467297253:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2can you find the height using the pythegorian theorem a²+b²=c² ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2ok, you are missing the leg or the hypotenuse here?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2So, you know one of the legs is 6, and the hypotenuse is 10, but you are missing another leg. Please plug this into a²+b²=c² (note: it doesn't mater which leg is a and which leg is b  the missing or the known leg)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2please take a shot to plug in numbers into a²+b²=c² (if you make a mistake it is ok, i will correct)

Falling_In_Katt
 one year ago
Best ResponseYou've already chosen the best response.1\[a ^{2}+6^{2}=12^{2} ?\] \[a ^{2}=108\] \[a=6\sqrt{3}\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2yes. a=√108 a=√(36•3) a=6√3 correct

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436467977322:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2This again shows the rule of a 30º60º90º, btw .... and in any case, you now have to find the area of 1/2 of this triangle

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436468071869:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2this is a smaller triangle, but a bigger triangle (that is twice greater) would have the area of 6•6√3, without dividing by 2.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2So your 4th face is 36√3.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2Now, your faces of the pyramid: you have three faces (side faces), of 48 each. AND a base (bottom face) of 36√3. So the total surface area of the pyramid (the sum of all of its face), is?

Falling_In_Katt
 one year ago
Best ResponseYou've already chosen the best response.1\[144+36\sqrt{3}\]?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2wolfram gives an estimate of 206.35 (or we can estimate √3 using a Taylor polynomial of function f(x)=√x, at a=4.... no I am just kidding.. would be to much....)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2you are done, that is your answer.... (for units though, I would add ":square units" or "units²" to denote that we found the area just now  (not volume pressure or other). )
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