PQRS is a rectangle, A, B, C and D are the mid points of sides PQ, QR, RS and PS respectively. If area of `Delta`PQR is 48 `cm^2`, then what is the area (in `cm^2`) of `Delta`BCD?

Options

A. 24
B. 6
C. 16
D. 12

Answer

To solve the problem, we need to find the area of triangle BCD given that the area of triangle PQR is 48 cm².

### Step-by-Step Solution:

1. **Understanding the Rectangle and Triangles**:
- PQRS is a rectangle.
- A, B, C, and D are the midpoints of sides PQ, QR, RS, and PS respectively.

2. **Area of Triangle PQR**:
- The area of triangle PQR is given as 48 cm².

3. **Identifying the Relationship**:
- Since A, B, C, and D are midpoints, triangles PAB, QBC, RCD, and SDA are formed within the rectangle.
- Triangle BCD is formed by connecting the midpoints of the sides of triangle PQR.

4. **Area of Triangle BCD**:
- Triangle BCD is similar to triangle PQR, and its area can be derived from the area of triangle PQR.
- The area of triangle BCD is one-fourth of the area of triangle PQR because the midpoints divide the triangle into smaller triangles of equal area.

5. **Calculating the Area**:
- Area of triangle BCD = (1/4) * Area of triangle PQR
- Area of triangle BCD = (1/4) * 48 cm²
- Area of triangle BCD = 12 cm².

### Final Answer:
The area of triangle BCD is **12 cm²**.