Given:
The radius of the circle is 10 cm
The central angle of the circle is (360 - 90)° = 270°
We need to determine the area of the composite figure.
Area of the composite figure:
The area of the figure can be determined using the area of the sector formula.
Thus, we have;
[tex]A=(\frac{\theta}{360}) \times \pi r^2[/tex]
Substituting [tex]\theta=270[/tex] and [tex]r=10[/tex] in the above formula, we get;
[tex]A=(\frac{270}{360}) \times (3.14) (10)^2[/tex]
Simplifying, we get;
[tex]A=(\frac{270}{360}) \times (314)[/tex]
Multiplying, we get;
[tex]A=\frac{84780}{360}[/tex]
Dividing the terms, we get;
[tex]A=235.5 \ cm^2[/tex]
Thus, the area of the composite figure is 235.5 cm²
Hence, Option C is the correct answer.
