The base of a regular pyramid is a hexagon.What is the area of the base of the pyramid?Enter your answer in the box. Express your answer in radical form. cm²
Accepted Solution
A:
ANSWER[tex] 96 \sqrt{3} {cm}^{2} [/tex]EXPLANATIONThe area of a regular polygon is[tex]Area= \frac{1}{2} ap[/tex]where 'a' is the apothem of the polygon and 'p' is the perimeter of the polygon.From the diagram,[tex] \sin(60) = \frac{a}{8} [/tex]a=8sin(60)[tex]a = 4 \sqrt{3} [/tex][tex] \cos(60) = \frac{l}{8} [/tex][tex]l = 8 \cos(60) [/tex][tex]l = 4[/tex]The length of one side of the hexagon is 2×4=8.The perimeter of the hexagon isp=6×8=48The area of the hexagon is[tex] = \frac{1}{2} \times 4 \sqrt{3} \times 48[/tex][tex] = 96 \sqrt{3} {cm}^{2} [/tex]