hello
i'll try to draw an image of the pyramid first
assuming the pyramid have a square base, we need to find the lengthof each side before we can find the volume of the pyramid
to find the value of x, we can assume a right angle triangle and use pythagora's theorem to solve for x
[tex]\begin{gathered} x^2=y^2+z^2 \\ 9.7^2=y^2+7.2^2 \\ 94.09=y^2+51.84 \\ y^2=94.09-51.84 \\ y^2=42.25 \\ \text{take the square root of both sides} \\ \sqrt{y^2}=\sqrt{42.25} \\ y=6.5 \end{gathered}[/tex]
the length of the square is to 2y since the base of the triangle = 2y
the volume of a pyramid can thus be calculated by 1/3LSH
L= length of base
S= slant height
H= height
[tex]\begin{gathered} \text{vol. of a pyramid }=\frac{1}{3}\times L\times S\times H \\ \text{vol. of a pyramid}=\frac{1}{3}\times13\times7.2\times9.7 \\ \text{vol. }=\frac{1}{3}\times907.92 \\ \text{volume of the pyramid = 302.64} \end{gathered}[/tex]
the volume of the given pyramid is 302.64 inches
