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 answer:

S =  192 cm²

Step-by-step explanation:

$$\begin{gathered} S_2=32{\text{cm}}^2 \\ {S}_2=\frac{a\cdot h}{2} \\ a=h \\ {S}_2=a^2/2 \\ a=\sqrt{2\cdot S_2}=\sqrt{2\cdot 32}=8\text{cm} \\ {S}_1=a^2=8^2=64{\text{cm}}^2 \\ S=4\cdot S_2+S_1=4\cdot 32+64=192{\text{cm}}^2 \end{gathered}$$

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