Answer:
[tex]6.28x^{2}[/tex] (as a decimal)
or
[tex]2\pi x^{2}[/tex] (in terms of pi)
Step-by-step explanation:
To solve this we are using the formula for the area of a semi-circle:
[tex]A=\frac{1}{2} \pi r^{2}[/tex]
where
[tex]A[/tex] is the area of the semi-circle
[tex]r[/tex] is the radius of the semi-circle
We know from our problem that our semi-circle has a radius of 2x, so [tex]r=2x[/tex]. Let's replace that value in our formula to find [tex]A[/tex]:
[tex]A=\frac{1}{2} \pi r^{2}[/tex]
[tex]A=\frac{1}{2} \pi (2x)^{2}[/tex]
[tex]A=\frac{1}{2} \pi 4x^{2}[/tex]
[tex]A=2\pi x^{2}[/tex]
[tex]A=6.28x^{2}[/tex]
We can conclude that the area of a semicircle that has a radius of 2x is [tex]2\pi x^{2}[/tex] (in terms or pi) or as a decimal: [tex]6.28x^{2}[/tex].
