Pyramid 4sides

Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.

Correct answer:

V =  37.3333 cm³
S =  74.2409 cm²

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ h=7\text{ cm } \\ {S}_1=a^2=4^2=16{\text{cm}}^2 \\ V=S_1\cdot h\mathrm{/}3=16\cdot 7\mathrm{/}3={\displaystyle \frac{112}{3}}=37.3333{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} h_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{7^2+(4\mathrm{/}2{)}^2}=\sqrt{53}\text{ cm}\doteq 7.2801\text{ cm } \\ {S}_2=a\cdot h_2\mathrm{/}2=4\cdot 7.2801\mathrm{/}2=2\sqrt{53}{\text{cm}}^2\doteq 14.5602{\text{cm}}^2 \\ S=S_1+4\cdot S_2=16+4\cdot 14.5602=74.2409{\text{cm}}^2 \end{gathered}$$

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