In a `Delta ABC, D, E and F` are the mid-point of sides BC, CA and AB respectively. If area of `Delta ABC = 16 cm^(2)`, find the area of trapezium FBCE

Answer

To find the area of trapezium FBCE in triangle ABC where D, E, and F are the midpoints of sides BC, CA, and AB respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The area of triangle ABC is given as \( 16 \, \text{cm}^2 \).
- Points D, E, and F are the midpoints of sides BC, CA, and AB respectively.

2. **Understand the Relationship of Areas:**
- Since D, E, and F are midpoints, triangle AEF is formed by connecting these midpoints.
- The area of triangle AEF is \( \frac{1}{4} \) of the area of triangle ABC because the midpoints divide the triangle into four smaller triangles of equal area.

3. **Calculate the Area of Triangle AEF:**
- Area of triangle AEF = \( \frac{1}{4} \times \text{Area of triangle ABC} \)
- Area of triangle AEF = \( \frac{1}{4} \times 16 \, \text{cm}^2 = 4 \, \text{cm}^2 \)

4. **Calculate the Area of Trapezium FBCE:**
- The area of trapezium FBCE can be found by subtracting the area of triangle AEF from the area of triangle ABC.
- Area of trapezium FBCE = Area of triangle ABC - Area of triangle AEF
- Area of trapezium FBCE = \( 16 \, \text{cm}^2 - 4 \, \text{cm}^2 = 12 \, \text{cm}^2 \)

5. **Final Answer:**
- The area of trapezium FBCE is \( 12 \, \text{cm}^2 \).