Square pyramid

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.

Final Answer:

S =  5035.3457 mm²

Step-by-step explanation:

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

Try another example