4side pyramid

Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.

Correct result:

V =  18.47 cm³
S =  48 cm²

Solution:

$$\begin{gathered} a=4cm \\ h=(a\mathrm{/}2)\cdot \tan 60^{\circ }=3.464cm \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=4cm \\ V={\displaystyle \frac{1}{3}}{a}^{2}h=18.47{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_1=a{h}_2\mathrm{/}2=8 \\ S=4\cdot S_1+a^2=48{\text{cm}}^2 \end{gathered}$$

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