Geometric Principle and Calculation

To solve this problem, we use a key geometric theorem regarding the area of parallelograms.

1. The Relevant Geometric Theorem

The theorem states that parallelograms that are on the same base and lie between the same parallel lines are equal in area.

• In the given figure, both parallelogram ABCD and parallelogram ABEF share the same base, AB.
• They also lie between the same two parallel lines: the line containing the base AB and the line containing the top side DE.

Therefore, according to the theorem, the area of parallelogram ABCD is equal to the area of parallelogram ABEF.

2. Using the Given Information

We are given:

• Area of parallelogram ABCD = 208 cm².
• This means the Area of parallelogram ABEF is also 208 cm².
• From the figure, the length of the base AB is 13 cm.

3. Calculating the Height

The formula for the area of a parallelogram is: Area = Base × Height.

We can now calculate the height of parallelogram ABEF:

208 cm² = 13 cm × Height

Height = 208 / 13

Height = 16 cm

Conclusion

The height of the parallelogram ABEF is 16 cm.