Answer:
The area of the Patrick's building is [tex]2340.22 ft^2[/tex].
Step-by-step explanation:
Shape of the Patrick's building = Decagon
In the figure attached:
Radius of the decagon = r = 12 feet
Side of the decagon = a
Angle AOB = 36°
Using trigonometric ratio is triangle AOC :
AO = r = 12 feet
AC = [tex]\frac{a}{2}=0.5a[/tex]
[tex]\tan \theta=\frac{Perpendicular}{base}[/tex]
[tex]\tan 36^o=\frac{0.5a}{12 feet}[/tex]
[tex]a=\frac{\tan 36^o\times 12 feet}{0.5}=17.44 feet[/tex]
Area of decagon :
[tex]A=\frac{5}{2}a^2\times \sqrt{5+2\sqrt{5}}[/tex]
[tex]A=\frac{5}{2}(17.44 ft)^2\times \sqrt{5+2\sqrt{5}}[/tex]
[tex]A=2340.22 ft^2[/tex]
The area of the Patrick's building is [tex]2340.22 ft^2[/tex].
