Perpendicular 35183

Calculate the surface and volume of a vertical prism if its height h = 18 cm and if the base is an equilateral triangle with side length a = 7.5 cm.

Correct answer:

S =  453.7139 cm²
V =  438.4254 cm³

Step-by-step explanation:

$$\begin{gathered} a=7.5\text{cm} \\ h=18\text{cm} \\ {S}_1=\frac{\sqrt{3}\cdot a^2}{4}=\frac{\sqrt{3}\cdot 7.5^2}{4}\doteq 24.357{\text{cm}}^2 \\ o=3\cdot a=3\cdot 7.5=\frac{45}{2}=22.5\text{cm} \\ S=2\cdot S_1+o\cdot h=2\cdot 24.357+22.5\cdot 18=453.7139{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot h=24.357\cdot 18=438.4254{\text{cm}}^3$

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