Final answer:
To find the area of the circle, we use the Pythagorean theorem to find the radius. Then, we use the formula A = πr^2 to calculate the area. In this case, the area is approximately 2826 cm^2.
Step-by-step explanation:
To find the area of the circle, we need to know the radius. Since O is the center, we can find the length of OP by using the Pythagorean theorem. The length of PQ is 24 cm and the length of RQ is 18 cm. We can use these lengths as the legs of a right triangle, with OP as the hypotenuse.
Using the Pythagorean theorem, OP = √(PQ^2 + RQ^2) = √(24^2 + 18^2) = √(576 + 324) = √900 = 30 cm.
The area of a circle is calculated using the formula A = πr^2, where r is the radius. In this case, the radius is 30 cm. So the area of the circle is A = π(30^2) = 900π cm^2. Using the approximate value of π as 3.14, the area is approximately 2826 cm^2.
Learn more about Finding the area of a circle