The tent

Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m.

Correct result:

S =  15 m²

Solution:

$$\begin{gathered} a=3\text{ m } \\ h=2\text{ m } \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{2^2+(3\mathrm{/}2{)}^2}={\displaystyle \frac{5}{2}}=2.5\text{ m } \\ {S}_1=a\cdot h_2\mathrm{/}2=3\cdot 2.5\mathrm{/}2={\displaystyle \frac{15}{4}}=3.75{\text{m}}^2 \\ S=4\cdot S_1=4\cdot 3.75=15{\text{m}}^2 \end{gathered}$$

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