Library / UKMT Senior Kangaroo /99 of 139

UKMT Senior Kangaroo, 2017

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The figure shows a quadrilateral $ABCD$ in which $AD = DC$ and $\angle ADC = \angle ABC = 90^\circ$ . The point $E$ is the foot of the perpendicular from $D$ to $AB$ . The length $DE$ is $25$ . What is the area of quadrilateral $ABCD$ ?

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.