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IMAS 2019–2020 Junior Division — First Round Question 17

IMAS · IMAS 2019–2020 Junior Division — First Round

Question 17

In rectangle $ABCD$, $AB=\sqrt3$ cm, $BC=3$ cm. Put a right triangle $DCE$ outside $ABCD$ and along edge $CD$ and $\angle CDE=30^\circ$. Flip along $AC$ such that $B$ lands at $K$. Join $KA$, $KC$, $KE$, $KD$, as in the figure. What is the area of the shaded region, in cm$^2$?

Question illustration
  1. $\frac32$
  2. $\frac{\sqrt3}{2}$
  3. $\frac{\sqrt3}{3}$
  4. $\sqrt3-1$
  5. $\frac{2\sqrt3}{3}$