Question

what is the area of the figures in a and b?

Explanation:

Step1: Identify shape A vertices

Vertices: $(-2, 5)$, $(2, 3)$, $(2, -3)$, $(-2, -5)$

Step2: Split shape A into 2 parts

Split into trapezoid (top) and trapezoid (bottom).
Top trapezoid bases: $8$ (vertical length from $y=-5$ to $y=5$ at $x=-2$), $6$ (vertical length from $y=-3$ to $y=3$ at $x=2$), height $4$ (horizontal distance from $x=-2$ to $x=2$).
Area of trapezoid: $\frac{1}{2} \times (b_1 + b_2) \times h$
Top trapezoid area: $\frac{1}{2} \times (8 + 6) \times 2 = 14$
Bottom trapezoid area: $\frac{1}{2} \times (8 + 6) \times 2 = 14$

Step3: Calculate total area of A

$14 + 14 = 28$

Step4: Identify shape B vertices

Vertices: $(-3, 3)$, $(2, 3)$, $(2, -5)$, $(-3, -5)$

Step5: Calculate area of B (rectangle)

Length: $5$ (horizontal distance from $x=-3$ to $x=2$), width: $8$ (vertical distance from $y=-5$ to $y=3$)
Area: $l \times w = 5 \times 8 = 40$

Answer:

Area of figure a: 28 square units
Area of figure b: 40 square units