In a certain regular square pyramid, all of the edges have length 12. Find the volume of the pyramid.

qwertyzz Sep 11, 2020

#2**0 **

Lets use (a^2)*(h/3).

h is calculated by finding the square’s diagonal (√(12^2 + 12^2) which comes to √288 or 12√2.

So, from the corner to the centre of the square is 6√2. This gives a right triangle with hypotenuse of 12 and base of 6√2.

12^2 - (6√2)^2 = 144 - 72. Therefore, the perpendicular height is √72 which is 6√2.

Plug that into the formula and get 144*((6√2)/3) which gives **144*(2√2) or 288√2**.

**A close decimal equivalent is 407.3 units^3**

Hope that helps!!

GrOoVyCoW Sep 11, 2020