Regular 4-sided pyramid

Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m.

Correct answer:

S =  1560.9191 m²

Step-by-step explanation:

$$\begin{gathered} h=20\text{ m } \\ {h}_2=23\text{ m } \\ (a\mathrm{/}2{)}^2+h^2=h_2^2=23^2=529 \\ a=2\cdot \sqrt{h_2^2-h^2}=2\cdot \sqrt{23^2-20^2}=2\sqrt{129}\text{ m}\doteq 22.7156\text{ m } \\ {S}_1=a^2=22.7156^2=516{\text{m}}^2 \\ {S}_2={\displaystyle \frac{a\cdot h_2}{2}}={\displaystyle \frac{22.7156\cdot 23}{2}}=23\sqrt{129}{\text{m}}^2\doteq 261.2298{\text{m}}^2 \\ S=S_1+4\cdot S_2=516+4\cdot 261.2298=1560.9191{\text{m}}^2 \end{gathered}$$

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