Calculate diagonals

Calculate the length of the solid diagonals of a prism with a rhombus base if the sizes of the base diagonals are 16 cm and 20 cm and the height of the prism is 32 cm. Calculate the size of the base edge.

Final Answer:

u₁ =  35.7771 cm
u₂ =  37.7359 cm
a =  12.8062 cm

Step-by-step explanation:

$$\begin{gathered} e=16\text{cm} \\ f=20\text{cm} \\ h=32\text{cm} \\ {u}_1=\sqrt{e^2+h^2}=\sqrt{16^2+32^2}=16\sqrt{5}=35.7771\text{cm} \end{gathered}$$

$u_2=\sqrt{f^2+h^2}=\sqrt{20^2+32^2}=4\sqrt{89}=37.7359\text{cm}$

$a=\sqrt{(e/2{)}^2+(f/2{)}^2}=\sqrt{(16/2{)}^2+(20/2{)}^2}=2\sqrt{41}=12.8062\text{cm}$

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