Solutions:

1. Area of Parallelogram GDEF

The area of a parallelogram is calculated using the formula:

$\text{Area} = \text{Base} \times \text{Height}$

For GDEF:

• Base ($b$) = $5 \, \text{m}$
• Height ($h$) = $3.2 \, \text{m}$

Substituting these values: $\text{Area} = 5 \times 3.2 = 16 \, \text{m}^2$

Answer: The area of parallelogram GDEF is 16 square meters.

2. Area of Parallelogram (Base = 17.9 cm, Height = 30.25 cm)

Using the same formula:

$\text{Area} = \text{Base} \times \text{Height}$

For the given parallelogram:

• Base ($b$) = $17.9 \, \text{cm}$
• Height ($h$) = $30.25 \, \text{cm}$

Substituting these values: $\text{Area} = 17.9 \times 30.25 = 541.475 \, \text{cm}^2$

Answer: The area of this parallelogram is 541.475 square centimeters.

Questions to Explore:

1. How would the area change if the base or height is doubled?
2. Can a parallelogram’s area be calculated using side lengths and angles?
3. What are the units of the area in this formula, and why?
4. How does the formula for the area of a parallelogram relate to that of a rectangle?
5. What happens to the area of a parallelogram if the height is perpendicular to a different base?

Tip:

Always ensure the height is perpendicular to the base when calculating the area of a parallelogram!