Quadrangular prism

The quadrangular prism has a volume of 648 cm³. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?

Correct result:

h =  14.4 cm

Solution:

$$\begin{gathered} V=648{\text{cm}}^3 \\ a=10\text{ cm } \\ c=5\text{ cm } \\ v=6\text{ cm } \\ S=(a+c)\cdot v\mathrm{/}2=(10+5)\cdot 6\mathrm{/}2=45{\text{cm}}^2 \\ h=V\mathrm{/}S=648\mathrm{/}45={\displaystyle \frac{72}{5}}={\displaystyle \frac{72}{5}}\text{ cm}=14.4\text{ cm} \end{gathered}$$

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