Question

write a quadratic function for the area of the figure. then, find the area for the given value of x.

x = 19

a quadratic function for the area of the figure is a(x) = □. (simplify your answer.)

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), where \(r\) is the radius of the circle. In this case, the radius \(r = x\).

Step2: Substitute the radius into the formula

Substituting \(r=x\) into the formula \(A=\pi r^{2}\), we get \(A(x)=\pi x^{2}\).

Step3: Calculate the area when \(x = 19\)

When \(x = 19\), we substitute \(x\) into \(A(x)\): \(A(19)=\pi\times(19)^{2}\). Since \((19)^{2}=361\), then \(A(19)=361\pi\approx361\times3.14 = 1133.54\).

Answer:

A quadratic function for the area is \(A(x)=\pi x^{2}\). When \(x = 19\), the area is approximately \(1133.54\).