Four-sided 5917

Mr. Radomír had a misfortune during the last storm; a tree fell on his roof in the shape of a regular four-sided pyramid and destroyed it all. The roof has a base edge length of 8m and a side edge length of 15m.

How many m² of roofing will he have to buy?

Correct answer:

S =  231.3093 m²

Step-by-step explanation:

$$\begin{gathered} a=8\text{m} \\ s=15\text{m} \\ {u}_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 8=8\sqrt{2}\text{m}\doteq 11.3137\text{m} \\ h=\sqrt{s^2-(u_1/2{)}^2}=\sqrt{15^2-(11.3137/2{)}^2}=\sqrt{193}\text{m}\doteq 13.8924\text{m} \\ {h}_2=\sqrt{(a/2{)}^2+h^2}=\sqrt{(8/2{)}^2+13.8924^2}=\sqrt{209}\text{m}\doteq 14.4568\text{m} \\ {S}_1=a\cdot h_2/2=8\cdot 14.4568/2=4\sqrt{209}{\text{m}}^2\doteq 57.8273{\text{m}}^2 \\ S=4\cdot S_1=4\cdot 57.8273=16\sqrt{209}=231.3093{\text{m}}^2 \end{gathered}$$

Try another example