You have a square with side length 30.
So the area of the square will be 30*30 = 900.
Notice that the right side (with length 30 as well) is actually the length of the diameter of this semi circle.
We know that area of a circle is given by [tex]\rm \pi r^2[/tex]. So then the area of a semi circle is half of that: [tex]\rm \frac12 \pi r^2[/tex].
If the diameter of the semi circle is 30,
then the radius is 15.
We'll plug in the radial value of 15, and 3.14 for a good pi approximation and calculate the area of the semi circle: [tex]\rm \frac12(3.14)\left(15\right)^2=353.25[/tex]
The area of the shaded region will be the area of the entire square minus the area of the semi circle: [tex]\rm 900 - 353.25 = 546.75[/tex]
