Answer:
251.57 square millimeters
Step-by-step explanation:
we know that
A regular 24-gon can be divided into 24 congruent isosceles triangle
so
The area of a regular 24-gon is the same that the area of 24 congruent isosceles triangle
To find out the area of one isosceles triangle, apply the law of sines
[tex]A=\frac{1}{2}(r^2)sin(\theta)[/tex]
where
[tex]r=9\ mm[/tex]
[tex]\theta=\frac{360^o}{24}=15^o[/tex]
substitute
[tex]A=\frac{1}{2}(9^2)sin(15^o)=10.48\ mm^2[/tex]
Multiply by 24 to obtain the area of regular 24-gon
[tex]10.48(24)=251.57\ mm^2[/tex]
