3sides prism

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

Correct answer:

S =  1416 cm²

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ r=13\text{cm} \\ {h}_2=\sqrt{r^2-(a/2{)}^2}=\sqrt{13^2-(10/2{)}^2}=12\text{cm} \\ h=3\cdot h_2=3\cdot 12=36\text{cm} \\ {S}_1=a\cdot h_2/2=10\cdot 12/2=60{\text{cm}}^2 \\ {S}_2=(2\cdot r+a)\cdot h=(2\cdot 13+10)\cdot 36=1296{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 60+1296=1416{\text{cm}}^2 \end{gathered}$$

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