To calculate the perimeter of the given object, we need to consider the lengths of the sides and the arc segment.

1. Calculate the lengths of the line segments:

   The object consists of line segments $AD$, $DC$, and $CA$, and an arc segment $DC$.

   • Segment $AD$: $A(-2, 1) \quad \text{and} \quad D(-10, 28.2)$ The distance formula is given by: $\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ So, $AD = \sqrt{(-10 - (-2))^2 + (28.2 - 1)^2} = \sqrt{(-8)^2 + 27.2^2} = \sqrt{64 + 739.84} = \sqrt{803.84} \approx 28.3$

   • Segment $DC$: $D(-10, 28.2) \quad \text{and} \quad C(6, 28.2)$ Since the y-coordinates are the same, $DC = |x_2 - x_1| = |6 - (-10)| = 16$

   • Segment $CA$: $C(6, 28.2) \quad \text{and} \quad A(-2, 1)$ Using the distance formula again, $CA = \sqrt{(6 - (-2))^2 + (28.2 - 1)^2} = \sqrt{(8)^2 + 27.2^2} = \sqrt{64 + 739.84} = \sqrt{803.84} \approx 28.3$

2. Calculate the length of the arc segment $DC$:

   The arc length $s$ can be found using the formula: $s = r \theta$ where $r$ is the radius and $\theta$ is the central angle in radians.

   • The radius $r = 10$ (since $D$ and $C$ are on the circle centered at $B(-2, 18)$).
   • The central angle is $76^\circ$.

   Convert the angle from degrees to radians: $\theta = 76^\circ \times \left(\frac{\pi}{180}\right) \approx 1.3265 \text{ radians}$

   So, $s = 10 \times 1.3265 \approx 13.3$

3. Add the lengths to find the perimeter:

   $\text{Perimeter} = AD + DC + CA + s = 28.3 + 16 + 28.3 + 13.3 \approx 85.9$

Therefore, the perimeter of the object to the nearest tenth is 85.9 units.

Would you like more details or have any questions? Here are some follow-up questions you might consider:

1. How is the distance formula derived?
2. What are the properties of a circle's radius and its central angle?
3. How do you convert degrees to radians?
4. Can you explain how to calculate arc length in detail?
5. What are some real-world applications of calculating perimeters?

Tip: When calculating distances and lengths in coordinate geometry, always ensure you use consistent units and verify your computations for accuracy.