Measures 3162

What is the surface of a regular pyramid with a square base? If each edge of the base measures 40 mm, the pyramid's height is 44 mm, and the pyramid's height is 38 mm.

Correct answer:

S =  5035.3457 mm²

Step-by-step explanation:

$$\begin{gathered} a=40 \\ s=44 \\ h=38 \\ {S}_1=a^2=40^2=1600 \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{38^2+(40/2{)}^2}=2\sqrt{461}\doteq 42.9418 \\ {s}_2=\sqrt{h^2+(\sqrt{2}\cdot a/2{)}^2}=\sqrt{38^2+(\sqrt{2}\cdot 40/2{)}^2}=2\sqrt{561}\doteq 47.3709 \\ {S}_2=a\cdot h_2/2=40\cdot 42.9418/2=40\sqrt{461}\doteq 858.8364 \\ S=S_1+4\cdot S_2=1600+4\cdot 858.8364=5035.3457{\text{mm}}^2 \end{gathered}$$

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