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

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

When $x \geq 2$x≥2: $y = x - 2$y=x−2

When $x < 2$x<2: $y = 2 - x$y=2−x

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

For $x \geq 2$x≥2:

$$x - 2 = 2$$x−2=2

$$x = 4$$x=4

For $x < 2$x<2:

$$2 - x = 2$$2−x=2

$$x = 0$$x=0

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

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The bounded region forms a triangle with:

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

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Area $= \dfrac{1}{2} \times \text{base} \times \text{height}$=21​×base×height

Area $= \dfrac{1}{2} \times 4 \times 2$=21​×4×2

Area $= 4$=4

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