# Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.

Result

V =  144.338 cm3
S =  193.364 cm2

#### Solution:

$a = 10 \ cm \ \\ h = a = 10 = 10 \ cm \ \\ \ \\ S_{ 1 } = \dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2 = \dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 10^2 = 25 \ \sqrt{ 3 } \ cm^2 \doteq 43.3013 \ cm^2 \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 43.3013 \cdot \ 10 \doteq 144.3376 = 144.338 \ cm^3$
$r = \dfrac{ \sqrt{ 3 } }{ 6 } \doteq 0.2887 \ cm \ \\ h = \sqrt{ h^2+r^2 } = \sqrt{ 10.0042^2+0.2887^2 } \doteq 10.0042 \ cm \ \\ S_{ 2 } = \dfrac{ 1 }{ 2 } \cdot \ a \cdot \ h = \dfrac{ 1 }{ 2 } \cdot \ 10 \cdot \ 10.0042 \doteq 50.0208 \ cm^2 \ \\ \ \\ S = S_{ 1 } + 3 \cdot \ S_{ 2 } = 43.3013 + 3 \cdot \ 50.0208 \doteq 193.3638 = 193.364 \ cm^2$

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Reynie
Easy problem solving????????????????????????

#### Following knowledge from mathematics are needed to solve this word math problem:

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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