To find the area of the circle, we need to first find its radius, since the formula for the area of a circle is A = πr^2.
We know that the arc length is given by:
L = rθ
where L is the length of the arc, r is the radius of the circle, and θ is the angle (in radians) subtended by the arc at the center of the circle.
In this case, we are given L = 15.708 inches and θ = 100 degrees. However, we need to convert the angle to radians:
θ (in radians) = θ (in degrees) x (π/180) θ (in radians) = 100 x (π/180) θ (in radians) = 5π/9
Now we can use the formula for the arc length to solve for r:
L = rθ 15.708 = r(5π/9) r = 15.708 / (5π/9) r = 9
Finally, we can use the formula for the area of a circle to find the area:
A = πr^2 A = π(9)^2 A = 81π
Therefore, the area of the circle is approximately 254.47 square inches, assuming that we use the value of π rounded to two decimal places, which is a common approximation