Pyramid height

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

Result

V =  415.692 cm3

Solution:

a=12 cm h=20 cm  S1=34⋅ a2=34⋅ 122≐36 3 cm2≐62.3538 cm2 V=13⋅ S1⋅ h=13⋅ 62.3538⋅ 20≐240 3≐415.6922≐415.692 cm3a=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 \doteq 240 \ \sqrt{ 3 } \doteq 415.6922 \doteq 415.692 \ \text{cm}^3

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Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.
See also our trigonometric triangle calculator.

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