Hexagonal pyramid

Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.

Result

S =  23.872 dm²
V =  6.734 dm³

Solution:

$a=1.8 \ \text{dm} \ \\ v=2.4 \ \text{dm} \ \\ h_{ 1 }=a \cdot \ \sqrt{ 3 }/2=1.8 \cdot \ \sqrt{ 3 }/2 \doteq 1.5588 \ \text{dm} \ \\ h_{ 2 }=\sqrt{ v^2+h_{ 1 }^2 }=\sqrt{ 2.4^2+1.5588^2 } \doteq 2.8618 \ \text{dm} \ \\ \ \\ S_{ 1 }=a \cdot \ h_{ 1 }/2=1.8 \cdot \ 1.5588/2 \doteq 1.403 \ \text{dm}^2 \ \\ S_{ 2 }=6 \cdot \ S_{ 1 }=6 \cdot \ 1.403 \doteq 8.4178 \ \text{dm}^2 \ \\ S_{ 3 }=a \cdot \ h_{ 2 }/2=1.8 \cdot \ 2.8618/2 \doteq 2.5756 \ \text{dm}^2 \ \\ S=S_{ 2 } + 6 \cdot \ S_{ 3 }=8.4178 + 6 \cdot \ 2.5756 \doteq 23.8716 \doteq 23.872 \ \text{dm}^2$

$V=\dfrac{ 1 }{ 3 } \cdot \ S_{ 2 } \cdot \ v=\dfrac{ 1 }{ 3 } \cdot \ 8.4178 \cdot \ 2.4 \doteq 6.7342 \doteq 6.734 \ \text{dm}^3$

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