Quadrilateral 39333

The tent with the floor has the shape of a regular quadrilateral pyramid with a base edge a = 2.4 m and a height of 1.8 m. How much canvas is needed for the tent?

Correct answer:

S =  16.144 m²

Step-by-step explanation:

$$\begin{gathered} a=2.4\text{m} \\ h=1.8\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{1.8^2+(2.4/2{)}^2}\doteq 2.1633\text{m} \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{2.4\cdot 2.1633}{2}\doteq 2.596{\text{m}}^2 \\ {S}_2=a^2=2.4^2=\frac{144}{25}=5.76{\text{m}}^2 \\ S=4\cdot S_1+S_2=4\cdot 2.596+5.76=16.144{\text{m}}^2 \end{gathered}$$

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