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V = 1/3 (base area)(height)
V = 1/3 (base area)(12)
I need help finding the base area

So, A = (12*12)/2 = 72

SA: 1/2bh(number of sides)
SA: 1/2(12)(12)(4)
SA: 1/2(144)(4)
SA: 72*4
SA: 288

Hero's formula is needed to solve this problem but I don't know how.

@jim_thompson5910 Can you please help solve this problem?

Okay so,
\[\frac{ \sqrt{3} }{ 4 }*12^2\]
= 62.4

62.3538290724796 which turns into 62.4 if you round to 1 decimal place
looks good

that's the area of the base

Volume of pyramid = (1/3)*(area of base)*(height of pyramid)

also why did you use 12 for the height, when the height is 11.5?

SA = Base area + 1/2 bln

SA = 62.4 + 1/2 (12)(12)(4)

you have one base face
and 3 lateral faces

So the answer is 278.4?

yeah approximately

Okay, so if it doesn't say that it is a square pyramid then it has 3 lateral faces?

the key word "triangular" in "triangular pyramid" means the base is a triangle

if they said "rectangular pyramid", then the base is a rectangle (4 lateral sides)

if they said "pentagonal pyramid" then the base is a pentagon with 5 lateral sides

yeah it's hard to convey 3D shapes on a flat 2D page

I do have something similar to those. Thanks!

no problem