Question

Ritu wants to make a trapezium such that \(AB\) is parallel to \(CD\). \(\angle ABC=90^\circ\) and \(\angle BAD=45^\circ\). Lengths: \(CD=5\ \mathrm{cm}\) and \(BC=4\ \mathrm{cm}\). Find the area of the trapezium.

• A. \(20\ \mathrm{cm}^2\)
• B. None of these
• C. \(28\ \mathrm{cm}^2\)
• D. \(24\ \mathrm{cm}^2\)

Hint:

When one leg is perpendicular to the bases in a trapezium, that leg is the \textbf{height}. Use coordinates or projections with the given angle to recover the unknown base.