Question

answer attempt 2 out of 3
area = units²

Explanation:

Step1: Divide the figure

Divide the figure into a rectangle \(ABCO\), a rectangle \(DEFG\) (assuming appropriate points for the lower - left rectangle) and a trapezoid (the part between them).

Step2: Calculate the area of rectangle \(ABCO\)

The length of \(AB\) is \(5\) units (from \(x=- 2\) to \(x = 3\)) and the height (from \(y = 0\) to \(y = 4\)) is \(4\) units. The area of a rectangle \(A_{1}=l\times w\), so \(A_{1}=5\times4 = 20\) square units.

Step3: Calculate the area of the lower - left rectangle (assuming \(DEFG\))

The length is \(3\) units and the height is \(3\) units. The area \(A_{2}=3\times3=9\) square units.

Step4: Calculate the area of the trapezoid

The parallel sides of the trapezoid: let \(a = 2\) units and \(b = 3\) units, and the height \(h = 2\) units. The area of a trapezoid \(A_{3}=\frac{(a + b)h}{2}=\frac{(2 + 3)\times2}{2}=5\) square units.

Step5: Sum up the areas

\(A=A_{1}+A_{2}+A_{3}\)
\(A=20 + 9+5\)

Answer:

\(34\)