3sides prism

The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.

Correct result:

S =  1416 cm²

Solution:

$$\begin{gathered} a=10\text{ cm } \\ r=13\text{ cm } \\ h=\sqrt{r^2-(a\mathrm{/}2{)}^2}=\sqrt{13^2-(10\mathrm{/}2{)}^2}=12\text{ cm } \\ {S}_1=a\cdot h\mathrm{/}2=10\cdot 12\mathrm{/}2=60{\text{cm}}^2 \\ {S}_2=(2\cdot r+a)\cdot 3\cdot h=(2\cdot 13+10)\cdot 3\cdot 12=1296{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 60+1296=1416{\text{cm}}^2 \end{gathered}$$

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