Quadrilateral pyramid

Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.

Correct answer:

S =  196.1444 cm²

Step-by-step explanation:

$$\begin{gathered} h=10\text{ cm } \\ a=8\text{ cm } \\ b=6\text{ cm } \\ {h}_1=\sqrt{h^2+(b\mathrm{/}2{)}^2}=\sqrt{10^2+(6\mathrm{/}2{)}^2}=\sqrt{109}\text{ cm}\doteq 10.4403\text{ cm } \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{10^2+(8\mathrm{/}2{)}^2}=2\sqrt{29}\text{ cm}\doteq 10.7703\text{ cm } \\ {S}_1={\displaystyle \frac{a\cdot h_1}{2}}={\displaystyle \frac{8\cdot 10.4403}{2}}=4\sqrt{109}{\text{cm}}^2\doteq 41.7612{\text{cm}}^2 \\ {S}_2={\displaystyle \frac{b\cdot h_2}{2}}={\displaystyle \frac{6\cdot 10.7703}{2}}=6\sqrt{29}{\text{cm}}^2\doteq 32.311{\text{cm}}^2 \\ S=2\cdot S_1+2\cdot S_2+a\cdot b=2\cdot 41.7612+2\cdot 32.311+8\cdot 6=196.1444{\text{cm}}^2 \end{gathered}$$

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