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 answer:

S =  15 m²

Step-by-step explanation:

$$\begin{gathered} a=3\text{m} \\ h=2\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{2^2+(3/2{)}^2}=\frac{5}{2}=2.5\text{m} \\ {S}_1=a\cdot h_2/2=a\cdot \frac{5}{2}/2=3\cdot 2.5/2=\frac{15}{4}=3.75{\text{m}}^2 \\ S=4\cdot S_1=4\cdot \frac{15}{4}=\frac{4\cdot 15}{4}=\frac{60}{4}=15{\text{m}}^2 \end{gathered}$$

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