Answer:
The volume of the right triangle pyramid is;
[tex]V=14.43\text{ }m^3[/tex]Explanation:
Given the right triangle pyramid whose base is 5 meters on each side and whose altitude 4 meters.
[tex]\begin{gathered} H=4 \\ a=b=c=5 \end{gathered}[/tex]Recall that the area of a pyramid can be calculated using the formula;
[tex]V=\frac{1}{3}AH[/tex]where;
A is the area of the base of the pyramid and H the altitute of the pyramid.
The area of the triangular base is;
[tex]A=\frac{1}{2}bh[/tex]the height of the base is;
[tex]\begin{gathered} h=\sqrt[]{5^2-2.5^2} \\ h=\sqrt[]{18.75} \\ h=4.33\text{ m} \end{gathered}[/tex]substituting to calculate the Volume of the pyramid;
[tex]\begin{gathered} V=\frac{1}{3}AH \\ V=\frac{1}{3}(\frac{1}{2}bh)H \\ V=\frac{1}{6}\text{bhH} \\ b=5\text{ m} \\ h=4.33\text{ m} \\ H=\text{ 4 m} \\ so; \\ V=\frac{1}{6}\times5\times4.33\times4 \\ V=14.43\text{ }m^3 \end{gathered}[/tex]Therefore, the volume of the right triangle pyramid is;
[tex]V=14.43\text{ }m^3[/tex]
