HMMT November

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 $\frac{1}{2}$ .

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