Pyramid surface calculation

Calculate the surface area of a regular quadrilateral pyramid given:
a= 3.2 cm h= 19 cm
Method:
1) calculation of the height of the side wall
2) area of the base
3) shell areas
4) the surface of a regular quadrilateral pyramid

Final Answer:

S =  132.2704 cm²

Step-by-step explanation:

$$\begin{gathered} a=3.2\text{cm} \\ v=19\text{cm} \\ {w}^2=v^2+(a/2{)}^2 \\ w=\sqrt{v^2+(a/2{)}^2}=\sqrt{19^2+(3.2/2{)}^2}\doteq 19.0672\text{cm} \\ {S}_1=a^2=3.2^2=\frac{256}{25}=10.24{\text{cm}}^2 \\ {S}_2=\frac{a\cdot w}{2}=\frac{3.2\cdot 19.0672}{2}\doteq 30.5076{\text{cm}}^2 \\ S=S_1+4\cdot S_2=10.24+4\cdot 30.5076=132.2704{\text{cm}}^2 \end{gathered}$$

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