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The base of a regular pyramid is a hexagon. The figure shows a regular hexagon with center C. An apothem is shown as a dashed segment perpendicular to an edge and is labeled as a. A dashed line segment joins the center with the left vertex of the edge perpendicular to the apothem. This segment has a length of 12 centimeters. The angle formed by the apothem and the segment measures 30 degrees. What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form. cm²

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Matheng
Length of the hexagon edge = the length of the line segment joins the center with any vertex of the hexagon

∴ length of edge = 12 cm.
and
length of apothem = [tex] \frac{ \sqrt{3} }{2} * length\ of \ edge = \frac{ \sqrt{3} }{2}*12 = 6 \sqrt{3} [/tex]

∴ area = 3 * edge * apothem
∴ [tex]area = 3 * 12 * 6 \sqrt{3} = 216 \sqrt{3} [/tex] cm²
dragonlovecall777

Answer:

216 (square root) 3 cm^2

Step-by-step explanation:

I just took the test!!!

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