The diagram shows the design for a decorative glass panel in the shape of a semicircle with center O O\,O and diameter AOEAOEAOE. The points B B\,B and D D\,D lie on the arc of the semicircle such that the chord BD BD\,BD is parallel to the diameter AEAEAE. A specific section of the glass, a segment labeled RRR, is bounded by the chord BD BD\,BD and the arc BCDBCDBCD. The radius of the semicircle is 8 cm and the angle DOE DOE\,DOE is 0.45 radians.
Show that, to 3 decimal places, the angle BOD BOD\,BOD is 2.242 radians.
Find the area of the shaded glass segment RRR, giving your answer in cm2\text{cm}^2cm2 to one decimal place.
Find the perimeter of the shaded region RRR, giving your answer in cm\text{cm}cm to one decimal place.
