Triangular prism

Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm

Correct result:

S =  264.4972 cm²

Solution:

$$\begin{gathered} h=10\text{ cm } \\ a=6\text{ cm } \\ b=8\text{ cm } \\ c=8\text{ cm } \\ o=a+b+c=6+8+8=22\text{ cm } \\ s=o\mathrm{/}2=22\mathrm{/}2=11\text{ cm } \\ {S}_1=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}=\sqrt{11\cdot (11-6)\cdot (11-8)\cdot (11-8)}=3\sqrt{55}{\text{cm}}^2\doteq 22.2486{\text{cm}}^2 \\ S=2\cdot S_1+o\cdot h=2\cdot 22.2486+22\cdot 10=264.4972{\text{cm}}^2 \end{gathered}$$

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