2022 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 21 Easy

A bowl is formed by attaching four regular hexagons of side 1 to a square of side 1. The edges of the adjacent hexagons coincide, as shown in the figure. What is the area of the octagon obtained by joining the top eight vertices of the four hexagons, situated on the rim of the bowl?

  • A.

    6

  • B.

    7

  • C.

    5+2\sqrt{2}

  • D.

    8

  • E.

    9

Answer:B

Create an tetraledron, each side of the  tetraledron gives an equilateral triangle.

A_{ABCD}=3\times3=9, A_{octagon}=8-4\times\frac12 \times\frac12=7.

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