In `Delta ABC`, E is mid-point of side AB and EBCD is a parallelogram. If the area of `Delta ABC` is 80 cm, find the area of parallelogram EBCD.

Answer

To solve the problem, we need to find the area of parallelogram EBCD given that the area of triangle ABC is 80 cm² and E is the midpoint of side AB.

### Step-by-Step Solution:

1. **Identify the Midpoint:**
Since E is the midpoint of side AB, we can denote the lengths as follows:
\[ AE = EB = \frac{AB}{2} \]

2. **Use the Area Formula for Triangle ABC:**
The area of triangle ABC can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, we can take AB as the base and EC as the height from point C to line AB. Therefore:
\[ \text{Area of } \triangle ABC = \frac{1}{2} \times AB \times EC \]

3. **Express Area in Terms of EB and EC:**
Since E is the midpoint, we can express AB as:
\[ AB = 2 \times EB \]
Substituting this into the area formula gives:
\[ \text{Area of } \triangle ABC = \frac{1}{2} \times (2 \times EB) \times EC = EB \times EC \]

4. **Set Up the Equation:**
We know from the problem that the area of triangle ABC is 80 cm². Therefore:
\[ EB \times EC = 80 \text{ cm}^2 \]

5. **Calculate the Area of Parallelogram EBCD:**
The area of parallelogram EBCD can be calculated using the base EB and height EC:
\[ \text{Area of parallelogram EBCD} = \text{base} \times \text{height} = EB \times EC \]
Since we established that \(EB \times EC = 80 \text{ cm}^2\), we find that:
\[ \text{Area of parallelogram EBCD} = 80 \text{ cm}^2 \]

### Final Answer:
The area of parallelogram EBCD is **80 cm²**.

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