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The diagram shows two right-angled triangles, \( \triangle ABD \) and \( \triangle ABC \). Here’s a step-by-step approach to solving for the area labeled "A" (in \( \triangle ABD \)):

### Step 1: Calculate the Area of Triangle ABD
Given:
- \( AB = 8 \) cm (base)
- \( AD = 12 \) cm (height)

The area \( A \) of triangle \( \triangle ABD \) is calculated as:

\[
A = \frac{1}{2} \times \text{base} \times \text{height} 
\]

\[
A = \frac{1}{2} \times 8 \, \text{cm} \times 12 \, \text{cm}
\]

\[
A = \frac{1}{2} \times 96 \, \text{cm}^2 
\]

\[
A = 48 \, \text{cm}^2
\]

### Final Answer:
The area of the triangle \( \triangle ABD \) is \( 48 \, \text{cm}^2 \).

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Would you like further details or have any other questions? Here are some additional related questions you might find interesting:

1. What is the area of triangle \( \triangle ABC \)?
2. How would you calculate the length of \( BC \) in triangle \( \triangle ABC \)?
3. How can you determine the perimeter of the quadrilateral \( ABDC \)?
4. What is the area of the entire quadrilateral \( ABDC \)?
5. How does the Pythagorean theorem apply to triangles \( \triangle ABD \) and \( \triangle ABC \)?

**Tip:** When solving for areas of right-angled triangles, always identify the base and height accurately as these are perpendicular to each other.

Learn how to calculate the area of triangle ABD using the formula A = 0.5 * base * height. This problem involves applying the Pythagorean theorem and is suitable for students in Grades 7-9.

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