# SOLUTION: To the nearest tenth find the volume of a regular hexagonal pyramid with base edges of 12cm long and height of 15cm

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 Question 1659: To the nearest tenth find the volume of a regular hexagonal pyramid with base edges of 12cm long and height of 15cmAnswer by AnlytcPhil(1277)   (Show Source): You can put this solution on YOUR website!To the nearest tenth find the volume of a regular hexagonal pyramid with base edges of 12cm long and height of 15cm ` Volume of a pyramid = Area of the base * Height * 1/3 ` So we begin by finding the area of the base. The base is a regular hexagon. A regular hexagon is 6 congruent equilateral triangles placed together like 6 pieces of pie: `__ /\/\ \/\/ ` The area of one equilateral triangle is given by A = bh/2. The base is the edge and the height is found by the Pythagorean theorem ` ` `/|\ 12/h| \12 `/_`|`_\ ` 6 ` 6 ` 6² + h² = 12² 36 + h² = 144 ` ` `h² = 144 - 36 ` ` `h² = 108 ` ` ` = ` So the area of one equilateral triangle with edge 12 is ` = ` The area of the regular hexagon base of the pyramid is then 6 times this, or ` Now since ` Volume of a pyramid = Area of the base * Height * 1/3, we have ` Volume = or, ` Edwin J