Pyramid four sides

A regular tetrahedral pyramid has a body height of 38 cm and a wall height of 42 cm. Calculate the surface area of the pyramid; the result is round to square centimeters.

Correct answer:

S =  4285 cm²

Step-by-step explanation:

$$\begin{gathered} h=38\text{cm} \\ s=42\text{cm} \\ {h}^2=s^2-(a/2{)}^2 \\ a=2\cdot \sqrt{s^2-h^2}=2\cdot \sqrt{42^2-38^2}=16\sqrt{5}\text{cm}\doteq 35.7771\text{cm} \\ {S}_1=a^2=35.7771^2=1280{\text{cm}}^2 \\ {S}_2=a\cdot s/2=35.7771\cdot 42/2=336\sqrt{5}{\text{cm}}^2\doteq 751.3188{\text{cm}}^2 \\ S=S_1+4\cdot S_2=1280+4\cdot 751.3188=4285{\text{cm}}^2 \end{gathered}$$

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