AMC 10 Step by Step

2014 AMC 10BProblem 21P21-25~6 minPrint

Quadrilaterals & Polygon Areas Triangles: Area & Pythagorean Apply an identity: SFFT, sum of squares, difference of cubes, Vieta Add construction lines/points (drop altitudes, extend segments, connect centers)

Trapezoid $ABCD$ has parallel sides $\overline{AB}$ of length $33$ and $\overline{CD}$ of length $21$ . The other two sides are of lengths $10$ and $14$ . The angles at $A$ and $B$ are acute. What is the length of the shorter diagonal of $ABCD$ ?