Question

each trapezoid in the figure below is congruent to trapezoid abdc. what is the perimeter of hexagon acefgh? 28 cm 32 cm 36 cm 64 cm figure may not be drawn to scale

Explanation:

Step1: Analyze the side lengths of the congruent trapezoids

Since each trapezoid is congruent to trapezoid \(ABDC\), we know that \(AC = 3\mathrm{cm}\), \(CE= 6\mathrm{cm}\), \(EF = 4\mathrm{cm}\), \(FG = 3\mathrm{cm}\), \(GH=6\mathrm{cm}\), \(HA = 4\mathrm{cm}\)

Step2: Calculate the perimeter of the hexagon

The perimeter \(P\) of a polygon is the sum of its side - lengths. For hexagon \(ACEFGH\), \(P=AC + CE+EF + FG+GH + HA\)
Substitute the values: \(P = 3+6 + 4+3+6 + 4\)

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Answer:

\(32\mathrm{cm}\)