Hello there. To solve this question, we'll need to remember some properties on geometry and areas of figures.
First, the area of a square is equal to the square of its side length.
The area of a circle is given by pi * the square of its radii, being this radii half of the diameter:
In this case, the side of the square is 1.5' and the diameter of the circle is 5.8'.
Finding the radii of the circle:
r = d/2 = 5.8'/2 = 2.9'
Calculating the area of the square and the circle
Asquare = 1.5² = 2.25 and Acircle = pi * 2.9² = pi * 8.41
The area of the shaded region is calculated by the difference between the area of the circle and the square
Ashaded = Acircle - Asquare
Ashaded = 8.41pi - 2.25
This is the area of the region we've been looking for.
