Surface of pyramid

In a regular quadrilateral pyramid, the height of the sidewall is equal to the length of the edge of the base. The content of the sidewall is 32 cm². What is the surface of the pyramid?

Correct result:

S =  160 cm²

Solution:

$$\begin{gathered} S_2=32{\text{cm}}^2 \\ {S}_2={\displaystyle \frac{a\cdot h}{2}} \\ a=h \\ {S}_2=a^2\mathrm{/}2 \\ a=\sqrt{2\cdot S_2}=\sqrt{2\cdot 32}=8\text{ cm } \\ {S}_1=a^2=8^2=64{\text{cm}}^2 \\ S=4\cdot S_2+S_1 \\ S=5\cdot S_2=5\cdot 32=160{\text{cm}}^2 \end{gathered}$$

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