Pyramid roof

3/5 of the lateral surface area of a regular quadrilateral pyramid with base edge 9 m and height 6 m has already been covered with roofing. How many square metres still need to be covered?

Final Answer:

S =  54 m²

Step-by-step explanation:

$$\begin{gathered} a=9\text{m} \\ h=6\text{m} \\ q=1-\frac{3}{5}=\frac{1\cdot 5}{5}-\frac{3}{5}=\frac{5}{5}-\frac{3}{5}=\frac{5-3}{5}=\frac{2}{5}=0.4 \\ {h}_1=\sqrt{h^2+(a/2{)}^2}=\sqrt{6^2+(9/2{)}^2}=\frac{15}{2}=7.5\text{m} \\ {S}_1=\frac{a\cdot h_1}{2}=\frac{9\cdot 7.5}{2}=\frac{135}{4}=33.75{\text{m}}^2 \\ S=q\cdot 4\cdot S_1=0.4\cdot 4\cdot 33.75=54{\text{m}}^2 \end{gathered}$$

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