2026 PCSS P2 Q3

2026 PCSS P2 Q3

Secondary 4
11 marks

The diagram below shows a circle of radius 2 cm inscribed in a regular hexagon.

    1. Show that the length of one side of the hexagon is 2.31 cm.[2]
    2. Find the area of the shaded region.[3]
  2. Two regular pentagons \(ABCDE\) and \(PQRST\) are joined together to form the shape shown below.
    Find angle \(AEC\).[3]
  3. The sides \(CD\) and \(AB\) are produced to meet at \(Z\). Show that triangle \(BZC\) is an isosceles triangle.[3]

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Answer:(a)(i) \(2.309401\ldots\text{ cm}\approx2.31\text{ cm}\) (shown) (ii) \(0.430\text{ cm}^2\) (b) \(72^\circ\) (c) \(\angle CBZ=\angle BCZ=72^\circ\), so \(BZ=CZ\) (shown)

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