Question

what is the area of the irregular hexagon? 49.4 cm², 57.12 cm², 74.24 cm², 80.38 cm²

Explanation:

Step1: Divide the hexagon into two trapezoids

A regular hexagon can be divided into two congruent trapezoids. The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height.

Step2: Identify the values for the trapezoid

For each trapezoid formed from the hexagon, the lengths of the parallel sides are $a = 4+4=8$ cm and $b = 4$ cm, and the height $h = 9.28$ cm.

Step3: Calculate the area of one trapezoid

Using the trapezoid area formula $A_1=\frac{(8 + 4)\times9.28}{2}=\frac{12\times9.28}{2}=55.68$ $cm^2$.

Step4: Calculate the area of the hexagon

Since the hexagon is composed of two such trapezoids, the area of the hexagon $A = 2\times A_1=2\times55.68 = 57.12$ $cm^2$.

Answer:

$57.12$ $cm^2$