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BeccaB003
 one year ago
Approximate the volume of the regular triangular pyramid if the height is approximately 11.5. (Remember that the base of a regular triangular pyramid must be an equilateral triangle, not necessarily congruent to the sides of the pyramid.)
828
239
717
BeccaB003
 one year ago
Approximate the volume of the regular triangular pyramid if the height is approximately 11.5. (Remember that the base of a regular triangular pyramid must be an equilateral triangle, not necessarily congruent to the sides of the pyramid.) 828 239 717

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BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1V = 1/3 (base area)(height) V = 1/3 (base area)(12) I need help finding the base area

taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.0Since the base is an equilateral triangle you can solve for the base area by using the formula A=(bxh)/2

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1So, A = (12*12)/2 = 72

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1V = 1/3 (72)(12) = 288 < But that isn't the correct answer. I got that answer last time I did this problem and it wasn't correct. I was told that I needed to use Hero's formula but I don't know how or why?!

NathalyN
 one year ago
Best ResponseYou've already chosen the best response.0SA: 1/2bh(number of sides) SA: 1/2(12)(12)(4) SA: 1/2(144)(4) SA: 72*4 SA: 288

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1That solves for the Surface area not the volume. @NathalyN

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1Hero's formula is needed to solve this problem but I don't know how.

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1@jim_thompson5910 Can you please help solve this problem?

taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.0Here is a link to how to use that formula: https://www.mathsisfun.com/geometry/heronsformula.html I've never heard of this before but I hope it helps

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1`Remember that the base of a regular triangular pyramid must be an equilateral triangle` the length of the bottom side is 12, so the other 2 sides must also be 12 too plug s = 12 into the area of an equilateral triangle formula \[\Large A = \frac{\sqrt{3}}{4}*s^2\]

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1Okay so, \[\frac{ \sqrt{3} }{ 4 }*12^2\] = 62.4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.162.3538290724796 which turns into 62.4 if you round to 1 decimal place looks good

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1that's the area of the base

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Volume of pyramid = (1/3)*(area of base)*(height of pyramid)

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1So, (1/3) * 62.4 * 12 = 249.6 < that isn't one of the answer options. It is closest to 239. Also, how did you find that formula for an equalateral triangle. Also, can I do this problem using Hero's formula because that is what I was told to use to get the correct answer. @jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1You can use hero's formula, but you'd get the same result if you used the formula I posted above this page shows how the formula is derived http://mathcentral.uregina.ca/QQ/database/QQ.09.03/jared1.html

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1also why did you use 12 for the height, when the height is 11.5?

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1Okay, thank you. Sorry, I didn't mean to use 12. I recalculated it and it and got 239. Thank you so much for your help! :)

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1Do you mind helping me with one more problem using the same image? Calculate the surface area of a regular triangular pyramid with the base edges of length 12 and a slant height of 12. (Remember that the base of a regular triangular pyramid must be an equilateral triangle, not necessarily congruent to the sides of the pyramid.)

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1SA = Base area + 1/2 bln

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1SA = 62.4 + 1/2 (12)(12)(4)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you have one base face and 3 lateral faces

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1we already have the area of the base face from last time the area of each face is (1/2)*b*h b = base of lateral face triangle = 12 h = height of lateral face triangle = 12

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the area of each lateral face is (1/2)*b*h b = base of lateral face triangle = 12 h = height of lateral face triangle = 12

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1Wait, I thought it had 4 sides not including the base. It is really hard to tell from the picture... So, it is SA = 62.4 + (1/2)(12)(12)(3)

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1So the answer is 278.4?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Rule for a pyramid (any pyramid) there is always one base face (usually on the ground) the lateral faces are triangles and there are n of them where the base is an ngon (example: n = 4, square pyramid has 4 lateral faces)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah approximately

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1Okay, so if it doesn't say that it is a square pyramid then it has 3 lateral faces?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the key word "triangular" in "triangular pyramid" means the base is a triangle

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if they said "rectangular pyramid", then the base is a rectangle (4 lateral sides)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if they said "pentagonal pyramid" then the base is a pentagon with 5 lateral sides

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1Oh! I see. I was really confused because by the picture it looks like there are four lateral sides. Thank you so much for your help! You clear everything up brilliantly! :D

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah it's hard to convey 3D shapes on a flat 2D page

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if you had these (maybe from a kit or something) http://bitplayer.org/wpcontent/uploads/2012/10/tetrahedrongeomags06601.jpg then it might be easier to visualize

BeccaB003
 one year ago
Best ResponseYou've already chosen the best response.1I do have something similar to those. Thanks!
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