Question

each trapezoid in the figure below is congruent to trapezoid abdc. what is the perimeter of hexagon acefgh? 3 cm 6 cm 4 cm (figure may not be drawn to scale ) 36 cm 64 cm 28 cm 32 cm

Explanation:

Step1: Analyze the side lengths of the hexagon

Since each trapezoid is congruent to trapezoid \(ABDC\), the side lengths of the hexagon \(ACEFGH\) can be determined from the given side lengths of trapezoid \(ABDC\). The sides of the hexagon are \(AC = 3\mathrm{cm}\), \(CE\) (equal to \(AB = 4\mathrm{cm}\)), \(EF\) (equal to \(BD\), and since \(BD\) is given as \(4\mathrm{cm}\) in the trapezoid's structure, \(EF = 4\mathrm{cm}\)), \(FG\) (equal to \(AC = 3\mathrm{cm}\)), \(GH\) (equal to \(AB = 4\mathrm{cm}\)), \(HA\) (equal to \(BD = 4\mathrm{cm}\)).

Step2: Calculate the perimeter

The perimeter \(P\) of a polygon is the sum of its side lengths. So \(P=AC + CE+EF + FG+GH + HA\). Substituting the values: \(P = 3+4 + 4+3+4+4\).

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Answer:

\(32\mathrm{cm}\)