The area of a right angled triangle ABC, right angled at B, is 46 sq units. A median is drawn from A to BC which intersects at D. Find the area (in sq. units) of triangle ABD.

Options

A. 12
B. 23
C. 46
D. 88

Answer

To solve the problem, we need to find the area of triangle ABD given that the area of triangle ABC is 46 square units and that a median is drawn from point A to side BC, intersecting at point D.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
Triangle ABC is a right-angled triangle with the right angle at B. The area of triangle ABC is given as 46 square units.

2. **Area of Triangle**:
The area of a triangle can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
However, we do not need to calculate the base and height directly since we already have the area.

3. **Median Properties**:
A median of a triangle divides it into two smaller triangles of equal area. Since AD is the median from A to side BC, it divides triangle ABC into two triangles: ABD and ACD.

4. **Calculating Areas of Triangles ABD and ACD**:
Since the median divides the area of triangle ABC equally, the areas of triangles ABD and ACD are equal. Therefore, we can express the area of triangle ABD as:
\[ \text{Area of } ABD = \frac{\text{Area of } ABC}{2} \]
Substituting the known area:
\[ \text{Area of } ABD = \frac{46}{2} = 23 \text{ square units} \]

5. **Final Answer**:
The area of triangle ABD is 23 square units.

### Summary:
The area of triangle ABD is 23 square units.