◢Circumscribed Triangle◣

$\text{area of blue region = area of the circle - area of the triangle}$

$\text{area of blue region} = \pi r^2 - \dfrac{1}{2}bh = \pi (5^2) - \dfrac{1}{2}(5)(5) \approx \boxed{66.040}$

To find the area, subtract out the area of the triangle from $\frac{1}{4}$ of the circular area, Then add $\frac{3}{4}$ of the area of the circle.

$Area = \frac{1}{4}π$ · $5^2$ - $\frac{5^2}{2}$ + $\frac{3}{4}π$ · $5^2$ ≈ $\boxed{66.0398}$