A designer is creating a specialized acoustic panel. The panel ABCDA ABCDA\,ABCDA consists of a major sector ACBA ACBA\,ACBA of a circle with centre C C\,C and radius 10 cm, and a triangular region ACDACDACD, as shown in the geometry below. The point D D\,D lies on the radius CBCBCB. The radius of the circle is 10 cm, the length of AD AD\,AD is 9 cm and the angle ACD ACD\,ACD is 0.8 radians0.8\text{ radians}0.8 radians.
Find the area of the major sector ACBAACBAACBA, giving your answer to one decimal place.
Given that the angle ADC ADC\,ADC is obtuse,
find the size of angle ADCADCADC, giving your answer to 3 decimal places.
Hence find the perimeter of the panel ABCDAABCDAABCDA, giving your answer to one decimal place.
