# Pyramid height

Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.

Correct result:

V =  415.692 cm3

#### Solution:

$a=12 \ \text{cm} \ \\ h=20 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 12^2 \doteq 36 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 62.3538 \ \text{cm}^2 \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 62.3538 \cdot \ 20=240 \ \sqrt{ 3 }=415.692 \ \text{cm}^3$

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