AMC 10 Daily Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 10 Easy

Six identical equilateral triangles of side length 2 are drawn outside a regular hexagon of side length 1, defining a larger hexagon as shown. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon?

  • A.

    5:1

  • B.

    6:1

  • C.

    7:1

  • D.

    8:1

  • E.

    9:1

Answer:C

Each yelllow equilateral triangle can be divided in to 4 unit equilateral triangles, for a total of 24 unit equilateral triangles. The small regular hexagon counts 6 unit equilateral triangles. Last, each white obtuse triangle is half of the area of a yellow equilateral trianlges, for a total of 3 yellow equilateral traingles, or 12 unit equilateral triangles.

The entire figure consists of 24+6+12=42 unit equilateral triangles. Therefore, the required ratio is 6:42=1:7.

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