Pyramid edge calculation

We know a regular quadrilateral pyramid's base diagonal length of u = 4 cm. The height of the pyramid is v = 5cm. Calculate the size of the side edge and the base edge of the pyramid.

Final Answer:

a =  2.8284 cm
s =  5.3852 cm

Step-by-step explanation:

$$\begin{gathered} u=4\text{cm} \\ v=5\text{cm} \\ {a}^2+a^2=u^2 \\ a=u/\sqrt{2}=4/\sqrt{2}=2\sqrt{2}=2.8284\text{cm} \end{gathered}$$

$$\begin{gathered} s^2=(u/2{)}^2+v^2=(4/2{)}^2+5^2=29 \\ s=\sqrt{(u/2{)}^2+v^2}=\sqrt{(4/2{)}^2+5^2}=\sqrt{29}=5.3852\text{cm} \end{gathered}$$

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