How to

How to find a total surface of a rectangular pyramid if each face is to be 8 dm high and the base is 10 dm by 6 dm.

Correct answer:

S =  202.0439 dm²

Step-by-step explanation:

$$\begin{gathered} a=10\text{ dm } \\ b=6\text{ dm } \\ h=8\text{ dm } \\ {h}_1=\sqrt{h^2+(b\mathrm{/}2{)}^2}=\sqrt{8^2+(6\mathrm{/}2{)}^2}=\sqrt{73}\text{ dm}\doteq 8.544\text{ dm } \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{8^2+(10\mathrm{/}2{)}^2}=\sqrt{89}\text{ dm}\doteq 9.434\text{ dm } \\ {S}_1={\displaystyle \frac{a\cdot h_1}{2}}={\displaystyle \frac{10\cdot 8.544}{2}}=5\sqrt{73}{\text{dm}}^2\doteq 42.72{\text{dm}}^2 \\ {S}_2={\displaystyle \frac{b\cdot h_2}{2}}={\displaystyle \frac{6\cdot 9.434}{2}}=3\sqrt{89}{\text{dm}}^2\doteq 28.3019{\text{dm}}^2 \\ B=a\cdot b=10\cdot 6=60{\text{dm}}^2 \\ S=2\cdot S_1+2\cdot S_2+B=2\cdot 42.72+2\cdot 28.3019+60=202.0439{\text{dm}}^2 \end{gathered}$$

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