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The question asks for the area of the shaded region in triangle \( ABC \), where points \( D, E, F, G, H, I \) divide the sides into three equal parts. The total area of triangle \( ABC \) is given as 630. Let's proceed by breaking down the problem.

### Key observations:
1. \( D, E, F, G, H, I \) are trisection points on the sides of triangle \( ABC \), meaning that the sides \( AB, BC, \) and \( CA \) are divided into three equal segments.
2. The shaded region involves smaller triangles within triangle \( ABC \), and due to the symmetry of the trisection, it can be solved geometrically using ratios.

### Step-by-step solution:
Since the sides are divided into three equal parts, the resulting smaller triangles are scaled-down versions of the main triangle \( ABC \), and the areas of these smaller triangles will follow certain fractional relationships relative to the total area.

By observing the triangles formed by the trisection points and the symmetry, we can estimate the area of the shaded region.

Let me compute this now.The area of the shaded region is \( 70 \). 

Would you like further details on how this solution was derived? Here are 5 related questions for further exploration:

1. What are the areas of the other non-shaded regions inside triangle \( ABC \)?
2. How does the trisection of triangle sides affect the areas of the smaller triangles?
3. What would the area of the shaded region be if triangle \( ABC \) had a different total area?
4. Can this method of division be generalized to polygons with more sides?
5. How would the result change if the points \( D, E, F, G, H, I \) were not trisection points but other divisions?

**Tip:** When dealing with symmetry in geometry, identifying proportional relationships between areas can simplify complex calculations.

如图，三角形ABC中，D、E、F、G、H、I是各边上的三等分点，若三角形ABC的面积为630，则阴影部分面积是多少？

In this geometry problem, we explore the area of a shaded region inside a triangle where the sides are divided into three equal segments. Given that the total area of triangle ABC is 630, this problem involves the application of symmetry, proportionality, and area ratios to find the solution. Suitable for Grades 9-11 students.

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