Quadrilateral pyramid

We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm.
Calculate
1/base content
2/casing content
3/pyramid surface
4/volume of the pyramid

Correct answer:

S₁ =  100 cm²
S₃ =  172.0465 cm²
S =  272.0465 cm²
V =  233.3333 cm³

Step-by-step explanation:

$$\begin{gathered} a=10\text{ cm } \\ v=7\text{ cm } \\ {S}_1=a^2=10^2=100{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} h_2=\sqrt{v^2+(a\mathrm{/}2{)}^2}=\sqrt{7^2+(10\mathrm{/}2{)}^2}=\sqrt{74}\text{ cm}\doteq 8.6023\text{ cm } \\ {S}_2=a\cdot h_2\mathrm{/}2=10\cdot 8.6023\mathrm{/}2=5\sqrt{74}{\text{cm}}^2\doteq 43.0116{\text{cm}}^2 \\ {S}_3=4\cdot S_2=4\cdot 43.0116=20\sqrt{74}=172.0465{\text{cm}}^2 \end{gathered}$$

$S=S_1+S_3=100+172.0465=272.0465{\text{cm}}^2$

$V={\displaystyle \frac{1}{3}}\cdot S_1\cdot v={\displaystyle \frac{1}{3}}\cdot 100\cdot 7={\displaystyle \frac{700}{3}}=233.3333{\text{cm}}^3$

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