Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.

Correct result:

V =  0.3183 m³
S =  3.5744 m²

Solution:

$$\begin{gathered} a=7\text{ dm}\to \text{ m}=7\mathrm{/}10\text{ m}=0.7\text{ m } \\ h=1.5\text{ m } \\ P={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 0.7^2\doteq 0.2122{\text{m}}^2 \\ V=P\cdot h=0.2122\cdot 1.5=0.3183{\text{m}}^3 \end{gathered}$$

$S=2\cdot P+3\cdot a\cdot h=2\cdot 0.2122+3\cdot 0.7\cdot 1.5=3.5744{\text{m}}^2$

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