Question

what is the area of the irregular hexagon? image of a hexagon with top and bottom sides labeled 5 cm, a horizontal dashed line labeled 9.28 cm, and two vertical segments (above and below the dashed line) each labeled 4 cm. below the hexagon, four multiple - choice options: 60.32 cm², 57.12 cm², 74.24 cm², 46.4 cm²

Explanation:

Step1: Recognize the shape as two trapezoids

The irregular hexagon can be divided into two congruent trapezoids. Each trapezoid has bases \(a = 5\space cm\), \(b = 9.28\space cm\) and height \(h = 4\space cm\).

Step2: Formula for area of a trapezoid

The area of a trapezoid is given by \(A_{trapezoid}=\frac{(a + b)}{2}\times h\).

Step3: Calculate area of one trapezoid

Substitute \(a = 5\), \(b = 9.28\), \(h = 4\) into the formula:
\(A_{trapezoid}=\frac{(5 + 9.28)}{2}\times4=\frac{14.28}{2}\times4 = 7.14\times4 = 28.56\space cm^{2}\)

Step4: Calculate area of the hexagon

Since there are two trapezoids, the area of the hexagon \(A = 2\times A_{trapezoid}\)
\(A = 2\times28.56 = 57.12\space cm^{2}\)

Answer:

\(57.12\space cm^{2}\) (corresponding to the option: 57.12 \(cm^{2}\))