Question

Need help finding the volumes of this pyramid please

Answer 1

Volume of pyramid = 1/3*AH, where A is the area of the base and H is the height

Since we are given three sides of the triangle (the base of the pyramid), we should use Heron formula: Area of a triangle = sq.root of(s(s - a)(s - b)(s - c)), where s is the semi-perimeter (ie. the perimeter divided by 2) and a, b and c are side lengths.
s = (5 + 12 + 13)/2
= 30/2 = 15
A = sq,root of(15(15 - 5)(15 - 12)(15 - 13))
= sq.root of (15*10*3*2)
= sq.root of 900
= 30 m^2

Volume = 1/3*AH
= 1/3*30*9
= 90 m^3