Answer:
[tex](25\pi\ -24)\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the circle minus the area of the two isosceles triangles
so
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
where r is the radius of the circle
In this problem we have
[tex]r=5\ cm[/tex]
substitute
[tex]A=\pi (5)^{2}[/tex]
[tex]A1=25\pi\ cm^{2}[/tex]
Find the area of the two triangles
The area of the two isosceles triangles is equal to
[tex]A=2[\frac{1}{2}bh]=bh[/tex]
we have
[tex]b=6\ cm[/tex]
[tex]h=5-1=4\ cm[/tex]
substitute
[tex]A2=6*4=24\ cm^{2}[/tex]
Find the area of the shaded region
[tex]A1-A2=(25\pi\ -24)\ cm^{2}[/tex]
