# Triangular prism

Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.

Result

S =  301.177 cm2

#### Solution:

$a=6 \ \text{cm} \ \\ h=15 \ \text{cm} \ \\ \ \\ S_{1}=3 \cdot \ a \cdot \ h=3 \cdot \ 6 \cdot \ 15=270 \ \text{cm}^2 \ \\ S_{2}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 6^2 \doteq 9 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 15.5885 \ \text{cm}^2 \ \\ \ \\ S=S_{1} + 2 \cdot \ S_{2}=270 + 2 \cdot \ 15.5885 \doteq 301.1769 \doteq 301.177 \ \text{cm}^2$

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