2026 PHS P2 Q8

2026 PHS P2 Q8

Secondary 4
7 marks

The diagram shows a quadrilateral, \(ABCD\).

\(AB=15\text{ cm}\), \(BC=8\text{ cm}\), \(AC=17\text{ cm}\), \(CD=13\text{ cm}\) and angle \(ADC=0.9\) radians.

The point \(M\) lies on \(AD\) such that \(AM:MD=3:4\).

  1. Show that angle \(ABC=\dfrac\pi2\) radians.[2]
  2. Find the size of angle \(ACD\).[3]
  3. Find the area of triangle \(AMC\).[2]

Solution:

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Answer:(a) \(\angle ABC=\dfrac\pi2\) (shown) (b) \(1.60\) radians (c) \(47.3\text{ cm}^2\)

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