Compound shape perimeter

A question is this type if and only if it asks to find the perimeter of a shape made from multiple sectors, triangles, or straight lines combined.

4 questions · Standard +0.3

1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta
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CAIE P1 2012 November Q6
7 marks Standard +0.3
6 \includegraphics[max width=\textwidth, alt={}, center]{e69332d0-2e45-4a86-a1f9-5d83bca1ad9b-2_526_659_1336_742} The diagram shows a sector \(O A B\) of a circle with centre \(O\) and radius \(r\). Angle \(A O B\) is \(\theta\) radians. The point \(C\) on \(O A\) is such that \(B C\) is perpendicular to \(O A\). The point \(D\) is on \(B C\) and the circular arc \(A D\) has centre \(C\).
  1. Find \(A C\) in terms of \(r\) and \(\theta\).
  2. Find the perimeter of the shaded region \(A B D\) when \(\theta = \frac { 1 } { 3 } \pi\) and \(r = 4\), giving your answer as an exact value.
CAIE P1 2022 March Q10
8 marks Standard +0.3
  1. Find the perimeter of the shaded region.
  2. Find the area of the shaded region.
CAIE P1 2021 November Q6
7 marks Standard +0.3
  1. Find the perimeter of the plate, giving your answer in terms of \(\pi\).
  2. Find the area of the plate, giving your answer in terms of \(\pi\) and \(\sqrt { 3 }\).
CAIE P1 2017 March Q4
6 marks Standard +0.3
  1. Show that angle \(C B D = \frac { 9 } { 14 } \pi\) radians.
  2. Find the perimeter of the shaded region.