Metal plate perimeter and area

Questions about shapes formed by removing segments from circles, requiring calculation of perimeters (combining arcs and chords) and areas (circle minus segments).

2 questions · Standard +0.3

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CAIE P1 2010 June Q7
8 marks Standard +0.3
7
\includegraphics[max width=\textwidth, alt={}, center]{71fe6352-e0dc-4c3a-8b54-99709a1782ca-3_744_675_255_735} The diagram shows a metal plate \(A B C D E F\) which has been made by removing the two shaded regions from a circle of radius 10 cm and centre \(O\). The parallel edges \(A B\) and \(E D\) are both of length 12 cm .
  1. Show that angle \(D O E\) is 1.287 radians, correct to 4 significant figures.
  2. Find the perimeter of the metal plate.
  3. Find the area of the metal plate.
CAIE P1 2012 June Q6
8 marks Standard +0.3
6
\includegraphics[max width=\textwidth, alt={}, center]{fa90db86-a73a-40db-b416-3c9f470fa207-3_446_645_258_751} The diagram shows a metal plate made by removing a segment from a circle with centre \(O\) and radius 8 cm . The line \(A B\) is a chord of the circle and angle \(A O B = 2.4\) radians. Find
  1. the length of \(A B\),
  2. the perimeter of the plate,
  3. the area of the plate.