Maths Olympiad Prep

Library / UKMT Junior Kangaroo /38 of 243

UKMT Junior Kangaroo, 2025

Geometry Difficulty 1.0 Junior Find the answer United Kingdom

Joseph draws a square with side-length 1010 cm. He joins the midpoints of the sides to make a smaller square, as shown in the diagram. What is the area, in cm2\text{cm}^2, of the smaller square?

(A) 1010 (B) 2020 (C) 3030 (D) 4040 (E) 5050

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.