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: Identify congruent sides

Since the trapezoids are congruent, corresponding sides are equal.

Step2: List side - lengths of the hexagon

The side - lengths of hexagon ACEFGH are composed of sides from the trapezoids. The lengths of the sides of the hexagon are: \(AC = 3\mathrm{cm}\), \(CE=4\mathrm{cm}\), \(EF = 6\mathrm{cm}\), \(FG=3\mathrm{cm}\), \(GH = 4\mathrm{cm}\), \(HA=6\mathrm{cm}\).

Step3: Calculate the perimeter

Perimeter \(P=3 + 4+6 + 3+4 + 6\).
\(P=(3 + 3)+(4 + 4)+(6 + 6)\)
\(P = 6+8 + 12\)
\(P=32\mathrm{cm}\)

Answer:

32 cm