Answer:
We can use the formula for the area of a circle and the information provided to find the approximate area of the circle.
The formula for the area of a circle is A = πr², where r is the radius of the circle.
We know that the distance from the center of the circle to the chord AB is 6 and the length of the chord AB is 10.
We can use the Pythagorean theorem to find the radius of the circle.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
So, we can use this theorem to find the radius of the circle as follows:
r² = (length of the chord /2)² + (distance of the chord to the center)²
r² = (10/2)² + 6²
r² = 25 + 36
r² = 61
r ≈ 7.8
Now that we know the radius of the circle, we can use the formula for the area of a circle to find the area of the circle:
A = πr²
A ≈ π (7.8)²
A ≈ 191.8
The approximate area of the circle is 192 square units.