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The diagram shows a triangle \(A B C\), where angle \(B A C\) is 0.9 radians. \(B A D\) is a sector of the circle with centre A and radius AB .
- The area of the sector \(B A D\) is \(16.2 \mathrm {~cm} ^ { 2 }\). Show that the length of \(A B\) is 6 cm .
- The area of triangle \(A B C\) is twice the area of sector \(B A D\). Find the length of \(A C\).
- Find the perimeter of the region \(B C D\).