Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid:
sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm
angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.)
S =? , V =?

Correct answer:

h =  10.3923 cm
S =  936 cm²
V =  1621.2 cm³

Step-by-step explanation:

$$\begin{gathered} S_3=a_1\cdot h_3\mathrm{/}2=18\cdot 18\mathrm{/}2=162{\text{cm}}^2 \\ {S}_4=a_2\cdot h_4\mathrm{/}2=6\cdot 6\mathrm{/}2=18{\text{cm}}^2 \\ S=4\cdot (S_3-S_4)+S_1+S_2=4\cdot (162-18)+324+36=936{\text{cm}}^2 \end{gathered}$$

$V=h\mathrm{/}3\cdot (S_1+\sqrt{S_1\cdot S_2}+S_2)=10.3923\mathrm{/}3\cdot (324+\sqrt{324\cdot 36}+36)=936\sqrt{3}=1621.2{\text{cm}}^3$

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