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.

Correct answer:

S =  301.1769 cm²

Step-by-step explanation:

$$\begin{gathered} a=6\text{ cm } \\ h=15\text{ cm } \\ {S}_1=3\cdot a\cdot h=3\cdot 6\cdot 15=270{\text{cm}}^2 \\ {S}_2={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 6^2=9\sqrt{3}{\text{cm}}^2\doteq 15.5885{\text{cm}}^2 \\ S=S_1+2\cdot S_2=270+2\cdot 15.5885=301.1769{\text{cm}}^2 \end{gathered}$$

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