The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}A_BH[/tex]
[tex]A_B[/tex] - area of a base
[tex]H[/tex] - height of a pyramid
Calculate the area of the base:
[tex]A_B=10^2=100\ u^2[/tex]
Calculate the length of height of the pyramid using the Pythagorean theorem:
[tex]H^2+5^2=13^2\\\\H^2=25=169\ \ \ |-25\\\\H^2=144\to H=\sqrt{144}\to H=12[/tex]
Calculate the volume of the pyramid:
[tex]V=\dfrac{1}{3}\cdot100\cdot12=100\cdot4=400\ u^3[/tex]
