2025 EOY Sec 1 AHS P1 Q5

1. In the figure below, the diameter of the circle, \(AB\), is \(42\) cm.

   \(DC\) is parallel to \(AB\) and \(AB:DC = 3:1\).

   \(DE = 20\) cm and is perpendicular to \(AB\).

   Given also that \(AD = BC = 22\) cm, find the area of the shaded region.

   [3]

2. In the figure, \(ABCD\) is a parallelogram, \(CD = 10\) cm and \(M\) is the midpoint of \(AB\). Given that the area of \(ABCD\) is \(60\) cm\(^2\), find

   1. the height of the parallelogram,

      [2]

   2. find the area of triangle \(CMB\).

      [1]

Source inconsistency in (a): a chord parallel to a diameter of a circle of radius 21 cm and 20 cm from the centre has length \(2\sqrt{21^2-20^2}=2\sqrt{41}\text{ cm}\), not 14 cm. Also, a trapezium with bases 42 cm and 14 cm, equal legs and height 20 cm would have leg length \(\sqrt{20^2+14^2}\text{ cm}\), not 22 cm. The intended area calculation below is conditional on the separately printed component dimensions; no exact figure satisfies all the labels. Part (b) is unaffected.