Wall height

Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.

Correct answer:

S =  132 cm²
V =  88.9944 cm³

Step-by-step explanation:

$$\begin{gathered} a=6 \\ v=0.8\cdot 10=8 \\ {S}_1=a^2=6^2=36 \\ {S}_2=a\cdot v\mathrm{/}2=6\cdot 8\mathrm{/}2=24 \\ S=S_1+4\cdot S_2=36+4\cdot 24=132{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} h=\sqrt{v^2-(a\mathrm{/}2{)}^2}=\sqrt{8^2-(6\mathrm{/}2{)}^2}=\sqrt{55}\doteq 7.4162 \\ V=S_1\cdot h\mathrm{/}3=36\cdot 7.4162\mathrm{/}3=12\sqrt{55}=88.9944{\text{cm}}^3 \end{gathered}$$

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