Answer:
83.7 %
Step-by-step explanation:
To get the area of the shaded region, we will following these steps.
Step one: Get the area of the sector of the circle.
The area of the sector of the circle can be obtained using the formula:
![Area = \frac{\theta}{360}\times \pi r^{2}](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Ctimes%20%5Cpi%20r%5E%7B2%7D)
Theta will be 60 degrees because triangle OAD is an equilateral triangle
Hence, ![Area = \frac{60}{360}\times \pi \times 9^{2}= 42.42cm^{2}](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B60%7D%7B360%7D%5Ctimes%20%5Cpi%20%5Ctimes%209%5E%7B2%7D%3D%2042.42cm%5E%7B2%7D)
Step Two: Get the area of the equilateral triangle
The area of the equilateral triangle can be got using the formula
![Area = \frac{1}{2} Base \times Height](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20Base%20%5Ctimes%20Height)
The height of the triangle can be got by drawing an imaginary line bisecting the triangle into two parts and applying the Pythagoras' theorem to any of the resulting right-angled triangles formed.
This will be ![height =\sqrt{4^{2}-2^{2}} =3.46cm](https://tex.z-dn.net/?f=height%20%3D%5Csqrt%7B4%5E%7B2%7D-2%5E%7B2%7D%7D%20%3D3.46cm)
Thus ![Area = \frac{1}{2}\times 4\times 3.46=6.93cm^{2}](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%204%5Ctimes%203.46%3D6.93cm%5E%7B2%7D)
Step Three: Subtract the area of the triangle from the area of the sector
Area of the shaded portion = ![42.42cm^{2}-6.93cm^{2}=35.49cm^{2}](https://tex.z-dn.net/?f=42.42cm%5E%7B2%7D-6.93cm%5E%7B2%7D%3D35.49cm%5E%7B2%7D)
Step Four: Divide the area of the shaded portion by the area of the entire shape and multiply the result by 100:
Expressing the ratio of the two areas as a percentage, we have
%