To solve the problem, we can follow these key steps:

Step 1: Key Observations

• AB is the diameter of the semicircle, so AB = 20 cm.
• C is on the semicircle, so the height from C to AB (let’s call it (h)) is the perpendicular distance from C to AB.
• The area of (\triangle ABC) is (\frac{1}{2} \times AB \times h).

Step 2: Area Equality

For (\triangle ABD) (with D on the extension of AB) to have the same area as (\triangle ABC), both triangles must share the same height (h) (since D is on the line AB, the height from C to AB is the same for both triangles).

Thus, their bases must be equal:
(AB = BD)

Since AB = 20 cm, BD = 20 cm.

Step 3: Calculate AD

AD = AB + BD = 20 cm + 20 cm = 40 cm.

Answer: (\boxed{40}) cm.

(\boxed{40})

作者声明:本文包含人工智能生成内容。