5
The diagram shows a triangle \(A B C\), in which angle \(A B C = 90 ^ { \circ }\) and \(A B = 4 \mathrm {~cm}\). The sector \(A B D\) is part of a circle with centre \(A\). The area of the sector is \(10 \mathrm {~cm} ^ { 2 }\).
- Find angle \(B A D\) in radians.
- Find the perimeter of the shaded region.