Quadrilateral pyramid

The regular quadrilateral pyramid has a surface of 260 cm² and a side wall area of 40 cm². Calculate the length of the base edge and the wall height.

Correct answer:

a =  10 cm
h₂ =  8 cm

Step-by-step explanation:

$$\begin{gathered} S=260{\text{cm}}^2 \\ {S}_1=40{\text{cm}}^2 \\ S=4\cdot S_1+P \\ P=S-4\cdot S_1=260-4\cdot 40=100{\text{cm}}^2 \\ P=a^2 \\ a=\sqrt{P}=\sqrt{100}=10\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=\frac{a\cdot h_2}{2} \\ {h}_2=2\cdot S_1/a=2\cdot 40/10=8\text{cm} \end{gathered}$$

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