Answer :
Based on the calculations, the area of the circle in terms of pi is equal to [tex]121\pi\;units^2[/tex]
Given the following data:
- Length of TA = 11 units.
- Angle CAT = 217 degrees.
How to calculate the area of a circle.
Mathematically, the circumference of a circle is given by the formula:
[tex]Area = \pi r^2[/tex]
Where:
- r is the radius of a circle.
Substituting the given parameter into the formula, we have;
[tex]Area = \pi \times 11^2\\\\Area = \pi \times 121\\\\Area =121\pi\;units^2[/tex]
The central angle of the shaded sector.
Based on the diagram, the sum of the central angles of both the shaded and non-shaded regions is equal to 360°. Thus, the central angle of the shaded region is given by:
[tex]x+217=360\\\\x=360-217[/tex]
x = 143°.
The area of the shaded sector.
Since the total area of the circle is given by a sector of 360°. Thus, the area of the shaded sector (143°) is given by:
[tex]\frac{A_{360}}{A_{143}} =\frac{121\pi}{A_{143}} = \frac{360}{143} \\\\121\pi \times 143=360\times A_{143}\\\\A_{143} = \frac{121\pi \times 143}{360} \\\\A_{143} = \frac{54358.98}{360} \\\\A_{143} = 151\;units^2[/tex]
Read more on circle here: brainly.com/question/14478195
