Pyramid a+h

Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.

Correct result:

S =  2376.1694 cm²
V =  6760 cm³

Solution:

$$\begin{gathered} a=26\text{ cm } \\ v=3\cdot 10=30\text{ cm } \\ {S}_1=a^2=26^2=676{\text{cm}}^2 \\ {h}_2=\sqrt{v^2+(a\mathrm{/}2{)}^2}=\sqrt{30^2+(26\mathrm{/}2{)}^2}=\sqrt{1069}\text{ cm}\doteq 32.6956\text{ cm } \\ {S}_2=a\cdot h_2\mathrm{/}2=26\cdot 32.6956\mathrm{/}2=13\sqrt{1069}{\text{cm}}^2\doteq 425.0424{\text{cm}}^2 \\ S=S_1+4\cdot S_2=676+4\cdot 425.0424=2376.1694{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot v\mathrm{/}3=676\cdot 30\mathrm{/}3=6760{\text{cm}}^3$

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