Isosceles + prism

Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm length of 3.7 cm

Correct result:

V =  116.6146 cm³

Solution:

$$\begin{gathered} h=17.5\text{ cm } \\ a=5.8\text{ cm } \\ r=3.7\text{ cm } \\ {h}_2=\sqrt{r^2-(a\mathrm{/}2{)}^2}=\sqrt{3.7^2-(5.8\mathrm{/}2{)}^2}\doteq 2.2978\text{ cm } \\ {S}_1={\displaystyle \frac{a\cdot h_2}{2}}={\displaystyle \frac{5.8\cdot 2.2978}{2}}\doteq 6.6637{\text{cm}}^2 \\ V=S_1\cdot h=6.6637\cdot 17.5=116.6146{\text{cm}}^3 \end{gathered}$$

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