Since the triangle is equilateral, all of its interior angles have a measure of 60º.
Substract the area of the triangle from the area of a circular sector with radius 7cm enclosed by an angle of 60º to find the area of the shaded region.
The area of an equilateral triangle with side length L is:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]
The area of a circular sector of radius r enclosed by an angle of θ degrees is:
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]
Replace θ=60 and r=7cm to find the area of the circular sector:
[tex]A_c=\frac{60}{360}\times3.14\times(7\operatorname{cm})^2=25.643\ldots cm^2[/tex]
Replace L=7cm to find the area of the triangle:
[tex]A_T=\frac{\sqrt[]{3}}{4}\times(7\operatorname{cm})^2=21.2176\ldots cm^2[/tex]
Then, the area of the shaded region is:
[tex]\begin{gathered} A_C-A_T=25.6433\ldots cm^2-21.2176\ldots cm^2 \\ =4.4257\ldots cm^2 \\ \approx4.43\operatorname{cm}^2 \end{gathered}[/tex]
Therefore, the area of the shaded region to 3 significant figures, is:
[tex]4.43\operatorname{cm}^2[/tex]
