# 3s prism

It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.

Correct result:

V =  414.735 cm3

#### Solution:

$a=7.1 \ \text{cm} \ \\ h=19.0 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 7.1^2 \doteq 21.8282 \ \text{cm}^2 \ \\ \ \\ V=S_{1} \cdot \ h=21.8282 \cdot \ 19=414.735 \ \text{cm}^3$

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