Competition problem — Geometry — Maths Olympiad Prep

Library / /8 of 740

Geometry Difficulty 4.0 AMC 10/12 Prove it United States

Problem:

Regular octagon $CHILDREN$ has area $1$ . Find the area of pentagon $CHILD$ .

Solution

Solution:

The pentagon $CHILD$ is congruent to the pentagon $NERDC$ , as their corresponding angles and sides are congruent. Moreover, the two pentagons together compose the entire octagon, so each pentagon must have area one-half of the area of the octagon, or $\frac{1}{2}$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.