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Trapezium Similarity: Side Ratios, Angles and Area

Trapezium Similarity: Side Ratios, Angles and Area

Secondary 2

Trapezium \(WXYZ\) is an enlargement of trapezium \(ABCD\). The lengths shown in figure below are in centimetres.

  1. Find the scale factor of the enlargement.
  2. Find \(\angle BCD\), stating your reason clearly.
  3. Given that the area of trapezium \(WXYZ\) is \(124.5\)cm\(^{2}\). Find the height of the trapezium \(WXYZ\).

Source check: similarity gives \(WX=1.5(2.3)=3.45\) cm. The perpendicular height of the trapezium cannot exceed this sloping side, but the printed area gives a height of \(20\) cm. Hence the area and side data are incompatible. The height answer is conditional on using the printed area and parallel-side lengths alone.

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Answer:\(\text{(a)}\ 1.5\) \(\text{(b)}\ 135^\circ\) \(\text{(c)}\ h=20\text{ cm}\) Results are conditional as explained in the source check; the complete printed givens are inconsistent.

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