Question

what is the area of this polygon? enter your answer in the box. \boxed{} units²

Explanation:

Step1: Identify polygon vertices

Vertices: $W(-4, -4)$, $C(4, -4)$, $S(4, -2)$, $N(2, 4)$, $F(-4, -2)$

Step2: Split into shapes: rectangle + trapezoid

Rectangle $WCSF$: width $8$, height $2$. Trapezoid $FSN$: bases $8, 6$, height $6$.

Step3: Calculate rectangle area

$\text{Area}_{\text{rectangle}} = 8 \times 2 = 16$

Step4: Calculate trapezoid area

$\text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (8 + 6) \times 6 = 42$

Step5: Sum the two areas

$\text{Total Area} = 16 + 42 = 58$

Answer:

58 units²