Diamond base

The prism with a diamond base has 24 cm and 20 cm long base diagonals. Calculate the height of a prism with a volume of 9.6 dm³ (cubic decimetres)

Correct answer:

h =  40 cm

Step-by-step explanation:

$$\begin{gathered} u_1=24\text{cm} \\ {u}_2=20\text{cm} \\ V=9.6{\text{dm}}^3\to {\text{cm}}^3=9.6\cdot 1000{\text{cm}}^3=9600{\text{cm}}^3 \\ S=\frac{u_1\cdot u_2}{2}=\frac{24\cdot 20}{2}=240{\text{cm}}^2 \\ h=V/S=9600/240=40\text{cm} \end{gathered}$$

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