Question

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

Explanation:

Step1: Identify congruent sides

Since the trapezoids are congruent, corresponding - side lengths are equal.

Step2: List side - lengths of the hexagon

The side - lengths of hexagon \(ACEFGH\) are composed of sides from the congruent trapezoids. The side - lengths are \(3\mathrm{cm}\), \(6\mathrm{cm}\), \(4\mathrm{cm}\), \(3\mathrm{cm}\), \(6\mathrm{cm}\), \(4\mathrm{cm}\).

Step3: Calculate the perimeter

Perimeter \(P=3 + 6+4 + 3+6 + 4\).
\[

$$\begin{align*} P&=(3 + 6+4)+(3 + 6+4)\\ &=13 + 13\\ &=26\mathrm{cm} \end{align*}$$

\]
However, there seems to be an error in the above - mentioned steps as we may have misinterpreted the figure. Let's re - evaluate.
The perimeter of the hexagon \(ACEFGH\):
We know that the non - parallel sides of the trapezoid are \(3\mathrm{cm}\) and \(4\mathrm{cm}\), and the parallel sides contribute lengths.
The perimeter \(P=(3 + 4)\times2+6\times2\)
\[

$$\begin{align*} P&=7\times2+12\\ &=14 + 12\\ &=28\mathrm{cm} \end{align*}$$

\]

Answer:

28 cm