CEMC Pascal

Geometry Difficulty 2.0 Junior Find the answer

Six rhombi of side length 1 are arranged as shown. What is the perimeter of this figure?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The first rhombus and the last rhombus each have three edges that form part of the exterior of the figure, and so they each contribute 3 to the perimeter. The inner four rhombi each have two edges that form part of the exterior of the figure, and so they each contribute 2 to the perimeter. Thus, the perimeter is $2 \times 3+4 \times 2=14$ .

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