Area of the bounded region between the curve $y = |x - 2|$ and the line $y = 2$ is:

The curve $y = |x - 2|$ is V-shaped with vertex at $(2, 0)$.

When $x \geq 2$: $y = x - 2$

When $x < 2$: $y = 2 - x$

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To find intersection points, solve $|x - 2| = 2$:

For $x \geq 2$:

$x - 2 = 2$

$x = 4$

For $x < 2$:

$2 - x = 2$

$x = 0$

Intersection points are $(0, 2)$ and $(4, 2)$.

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The bounded region forms a triangle with:

• Vertices at $(0, 2)$, $(4, 2)$, and $(2, 0)$
• Base = $4 - 0 = 4$ units
• Height = $2 - 0 = 2$ units

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Area $= \dfrac{1}{2} \times \text{base} \times \text{height}$

Area $= \dfrac{1}{2} \times 4 \times 2$

Area $= 4$

Therefore, the area of the bounded region is $4$ square units.