# Tetrahedral pyramid

A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).

Result

V =  83.467 cm3
S =  87.87 cm2

#### Solution:

$a = 6.5 \ cm \ \\ s = 7.5 \ cm \ \\ \ \\ S_{ 1 } = a^2 = 6.5^2 = \dfrac{ 169 }{ 4 } = 42.25 \ cm^2 \ \\ \ \\ u_{ 1 } = \sqrt{ 2 } \cdot \ a = \sqrt{ 2 } \cdot \ 6.5 \doteq 9.1924 \ cm \ \\ \ \\ h = \sqrt{ s^2 - (u_{ 1 }/2)^2 } = \sqrt{ 7.5^2 - (9.1924/2)^2 } \doteq 5.9266 \ cm \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 42.25 \cdot \ 5.9266 \doteq 83.4668 = 83.467 \ cm^3$
$h_{ 2 } = \sqrt{ h^2 + (a/2)^2 } = \sqrt{ 5.9266^2 + (6.5/2)^2 } \doteq 6.7593 \ cm \ \\ \ \\ S_{ 2 } = \dfrac{ 1 }{ 2 } \cdot \ a \cdot \ h_{ 2 } = \dfrac{ 1 }{ 2 } \cdot \ 6.5 \cdot \ 6.7593 \doteq 21.9676 \ cm^2 \ \\ \ \\ S = 4 \cdot \ S_{ 2 } = 4 \cdot \ 21.9676 \doteq 87.8703 = 87.87 \ cm^2$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

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