Answer:
The volume of a pentagonal pyramid is given below as
[tex]V=\frac{1}{3}\times area\text{ of base}\times\text{ height}[/tex]
Step 1:
The base is a pentagon which contains 5 regular triangles of same base
[tex]\begin{gathered} base=8cm \\ h=5.5cm \end{gathered}[/tex]
Area of a triangle is
[tex]\begin{gathered} A_{triangle}=\frac{1}{2\text{ }}\times base\text{ }\times height \\ A_{triangle}=\frac{1}{2}\times8cm\times5.5cm \\ A_{triangle}=22cm^2 \end{gathered}[/tex]
Then the area of the base will be
[tex]\begin{gathered} A_{base}=5\times area\text{ of each triangle} \\ A_{base}=5\times22cm^2 \\ A_{base}=110cm^2 \end{gathered}[/tex]
Therefore,
The volume of the pyramid will be
[tex]\begin{gathered} V_{pyramid}=\frac{1}{3}\times basearea\times height \\ V_{pyramid}=\frac{1}{3}\times110cm^2\times12cm \\ V_{pyramid}=440cm^3 \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow440[/tex]
