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UKMT Senior Kangaroo, 2024

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

An octahedron is inscribed in a cube of side-length 12. The vertices of the octahedron are at the centre of the faces of the cube. The surface area of the octahedron is $a \times \sqrt{b}$ , where $b$ is a prime number. What is the value of $a + 10b$ ?

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