This world needs more coin of such shape!

Geometry Level 5

The diagram above shows a Reuleaux septagon drawn from a regular septagon with circumradius 1, where arc $A_1 A_2$ is drawn from center $A_5$ , arc $A_2 A_3$ is drawn from center $A_6$ , arc $A_3 A_4$ is drawn from center $A_7$ , and so on.

Find the area of the Reuleaux septagon to 5 decimal places.

Bonus: Generalize this for all Reuleaux $n$ -gon where $n$ is an odd number.

Inspiration

This world needs more coin of such shape!

You may want to read up Reuleaux triangle first.

Image Credit: Wikimedia Reuleaux polygons by LEMeZza

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This world needs more coin of such shape!

You may want to read up Reuleaux triangle first.

Image Credit: Wikimedia Reuleaux polygons by LEMeZza

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.