Question

What is the area of semi circle that has a radius of 2x?

Answer 1

`6.28x^(2)` (as a decimal)

or

`2\pi x^(2)` (in terms of pi)

Explanation:

To solve this we are using the formula for the area of a semi-circle:

`A=(1)/(2) \pi r^(2)`

where

`A` is the area of the semi-circle

`r` is the radius of the semi-circle

We know from our problem that our semi-circle has a radius of 2x, so
`r=2x`. Let's replace that value in our formula to find
`A`:

`A=(1)/(2) \pi r^(2)`

`A=(1)/(2) \pi (2x)^(2)`

`A=(1)/(2) \pi 4x^(2)`

`A=2\pi x^(2)`

`A=6.28x^(2)`

We can conclude that the area of a semicircle that has a radius of 2x is
`2\pi x^(2)` (in terms or pi) or as a decimal:
`6.28x^(2)`.