Answer:
The area of the roof is 3.80 m².
Step-by-step explanation:
The lateral surface area of an octagonal pyramid is given by:
[tex]A = 2s(\sqrt{4h^{2} + 5.828s^{2}})[/tex] (1)
Where:
s: is the length of the base edge = 0.5 m
h: is the height
We can find the height from the slant height (S = 1.9 m):
[tex] S = \sqrt{h^{2} + 1.457s^{2}} [/tex] (2)
By solving equation (2) for "h" we have:
[tex] h = \sqrt{S^{2} - 1.457s^{2}} = \sqrt{(1.9)^{2} - 1.457(0.5)^{2}} = 1.80 m [/tex]
Now, we can calculate the area of the roof (equation 1):
[tex]A = 2s(\sqrt{4h^{2} + 5.828s^{2}}) = 2*0.5(\sqrt{4(1.80)^{2} + 5.828(0.5)^{2}}) = 3.80 m^{2}[/tex]
Therefore, the area of the roof is 3.80 m².
I hope it helps you!
