Tower roof

The tower's roof is a regular 4-sided pyramid with a height of 4m and an edge of the base of 6m. 25% of the roof covering was found to be damaged. How many square meters of coverage are needed to repair the roof?

Correct answer:

S =  15 m²

Step-by-step explanation:

$$\begin{gathered} h=4\text{m} \\ a=6\text{m} \\ q=25\%=\frac{25}{100}=\frac{1}{4}=0.25 \\ n=4 \\ {h}_1=\sqrt{h^2+(a/2{)}^2}=\sqrt{4^2+(6/2{)}^2}=5\text{m} \\ {S}_1=\frac{a\cdot h_1}{2}=\frac{6\cdot 5}{2}=15{\text{m}}^2 \\ {S}_4=n\cdot S_1=4\cdot 15=60{\text{m}}^2 \\ S=q\cdot S_4=0.25\cdot 60=15{\text{m}}^2 \end{gathered}$$

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