# Prism - eq triangle

Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.

Result

V =  41.569 cm3
S =  85.856 cm2

#### Solution:

$a=4 \ \\ h=6 \ \\ P=\sqrt{ 3 }/4 \cdot \ a^2=\sqrt{ 3 }/4 \cdot \ 4^2 \doteq 4 \ \sqrt{ 3 } \doteq 6.9282 \ \\ V=P \cdot \ h=6.9282 \cdot \ 6 \doteq 24 \ \sqrt{ 3 } \doteq 41.5692 \doteq 41.569 \ \text{cm}^3$
$S=2 \cdot \ P + 3 \cdot \ a \cdot \ h=2 \cdot \ 6.9282 + 3 \cdot \ 4 \cdot \ 6 \doteq 85.8564 \doteq 85.856 \ \text{cm}^2$

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