GIVEN:
We are given a regular pyramid with the following dimensions;
[tex]\begin{gathered} Base=6 \\ \\ Height=8 \end{gathered}[/tex]Required;
To calculate the lateral area.
Step-by-step solution;
To begin, we first take note that what we have is a regular pyramid with a hexagonal base. That is, the base has 6 sides.
Also, it is called a regular pyramid which means all sides of the base are equal.
We are given the formula for the lateral area as follows;
[tex]\begin{gathered} For\text{ }a\text{ }hexagonal\text{ }pyramid: \\ \\ Lateral\text{ }Area=3a\sqrt{h^2+\frac{3a^2}{4}} \end{gathered}[/tex]Where you have;
[tex]\begin{gathered} a=base \\ \\ h=height \end{gathered}[/tex]We now have;
[tex]Lateral\text{ }Area=3(6)\sqrt{8^2+\frac{3(6)^2}{4}}[/tex]Now we can simplify;
[tex]\begin{gathered} Lateral\text{ }Area=18\sqrt{64+\frac{3(36)}{4}} \\ \\ Lateral\text{ }Area=18\sqrt{64+27} \\ \\ Lateral\text{ }Area=18\sqrt{91} \\ \\ Lateral\text{ }Area=171.709056255 \end{gathered}[/tex]We can however write the "exact answer" as follows;
ANSWER:
[tex]L.A=18\sqrt{91}\text{ }units^2[/tex]