Question #105046
A lateral edge of the hexagonal pyramid is 2.0m long and its base perimeter is 6m determine the volume of the pyramid and its lateral area
1
Expert's answer
2020-03-10T11:16:05-0400

Volume of Hexagonal pyramid is given by 32a2h\dfrac{\sqrt3}{2}a^2h ; where a is the base edge and h is the height

base perimeter = 6*a

6=6*a

a=1 m

lateral edge =a2+h2\sqrt{a^2+h^2} =12+h2=2,=\sqrt{1^2+h^2}=2,

h=3h=\sqrt{3}

Volume = 32a2h\dfrac{\sqrt3}{2}a^2h =32123=3/2\dfrac{\sqrt3}{2}1^2\sqrt3=3/2


Lateral surface area = 3ah2+3a24=313+3/4=315/23a\sqrt{h^2+\dfrac{3a^2}{4}}=3*1*\sqrt{3+3/4}=3\sqrt{15}/2



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