Answer:
[tex]216\text{ feet}^2[/tex]
Step-by-step explanation:
We have been given that the base of a regular hexagonal pyramid has sides 6 feet long and a slant height of 12 feet. We are asked to find the lateral area of the pyramid.
[tex]\text{Lateral area of a regular pyramid}=\frac{1}{2}(p*l)[/tex], where,
p = Perimeter of base of pyramid,
l = Slant height.
Since each side of the the hexagonal base is 6 feet, so perimeter of base would be [tex]6*6=36[/tex] feet.
[tex]\text{Lateral area of a regular hexagonal pyramid}=\frac{1}{2}(36\times 12)[/tex]
[tex]\text{Lateral area of a regular hexagonal pyramid}=18\times 12[/tex]
[tex]\text{Lateral area of a regular hexagonal pyramid}=216[/tex]
Therefore, the lateral area of hexagonal pyramid would be 216 square feet.
