这道题如何解答，主要知识点是什么？---**Question Stem:** Q1: As shown in the figure, in triangle ABC, DC=2BD, CE=3AE, the area of triangle ADE is 20 square centimeters, what is the area of triangle ABC? **Chart/Diagram Description:** Type: Geometric figure (triangle). Main Elements: A triangle labeled ABC. Point D is on the side BC. Point E is on the side AC. Line segment AD connects vertex A to point D on BC. Line segment DE connects point D on BC to point E on AC. Points are labeled as A (top vertex), B (left base vertex), C (right base vertex), D (on BC between B and C), and E (on AC between A and C). Lines form the sides of triangle ABC (AB, BC, AC) and segments AD and DE within the triangle. Relative Position: D is located on BC. E is located on AC.

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Let's analyze this triangle area problem step by step. We have triangle ABC with point D on side BC and point E on side AC. We're given that DC equals 2BD, CE equals 3AE, and the area of triangle ADE is 20 square centimeters. We need to find the area of triangle ABC. The key principle for solving this problem is understanding area ratios. When two triangles share a common vertex, the ratio of their areas equals the ratio of their bases. First, let's find the ratio AE to AC. Since CE equals 3AE, we have AC equals AE plus CE, which is AE plus 3AE, giving us 4AE. Therefore, the ratio AE to AC is 1 to 4. Now let's calculate the area of triangle ADC. Triangles ADE and ADC share vertex D, and their bases AE and AC lie on the same line, so they have the same height from D. Using our area ratio formula, Area of ADE divided by Area of ADC equals AE divided by AC. Substituting our known values: 20 divided by Area of ADC equals 1 divided by 4. Solving this equation, we get Area of ADC equals 20 times 4, which is 80 square centimeters. Now let's find the ratio DC to BC and calculate the final answer. Given that DC equals 2BD, we have BC equals BD plus DC, which is BD plus 2BD, giving us 3BD. Therefore, the ratio DC to BC is 2BD divided by 3BD, which equals 2 to 3. For the final step, triangles ADC and ABC share vertex A, so their area ratio equals their base ratio. We have 80 divided by Area of ABC equals 2 divided by 3. Solving this, Area of ABC equals 80 times 3 divided by 2, which gives us 120 square centimeters. Let's summarize our solution. Starting with the given area of triangle ADE as 20 square centimeters, we found that AE to AC equals 1 to 4, which gave us the area of triangle ADC as 80 square centimeters. Then we calculated that DC to BC equals 2 to 3, leading to our final answer: the area of triangle ABC is 120 square centimeters. The key knowledge points are understanding that area ratios equal base ratios when triangles share a vertex, segment ratio calculations, and triangle area relationships. This systematic approach using area ratios is fundamental in geometry problem solving.