A real-life problem involving parallelograms with a PISA (Programme for International Student Assessment)-type question typically involves applying geometric concepts in practical situations. Below is an example:

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Scenario:

A farmer has a plot of land shaped like a parallelogram. The base of the parallelogram is 120 meters, and the height is 50 meters. The farmer wants to:

1. Calculate the area of the plot to decide how much fertilizer is needed.
2. Build a fence around the plot, so he needs to calculate its perimeter.

The two opposite sides of the parallelogram measure 120 meters and 80 meters.

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Questions:

1. Calculate the area of the plot.
The area $A$ of a parallelogram is given by:
$A = \text{base} \times \text{height}$
Substituting the values:
$A = 120 \, \text{m} \times 50 \, \text{m} = 6000 \, \text{m}^2$

2. Calculate the perimeter of the plot.
The perimeter $P$ is given by:
$P = 2 \times (\text{base} + \text{side length})$
Substituting the values:
$P = 2 \times (120 \, \text{m} + 80 \, \text{m}) = 2 \times 200 \, \text{m} = 400 \, \text{m}$

3. How much fencing does the farmer need?
The farmer will need $400 \, \text{m}$ of fencing (same as the perimeter).

4. If 1 kg of fertilizer covers 100 m², how much fertilizer is required?
The total amount of fertilizer required is:
$\text{Fertilizer needed} = \frac{\text{Area}}{\text{coverage per kg}}$
Substituting the values:
$\text{Fertilizer needed} = \frac{6000 \, \text{m}^2}{100 \, \text{m}^2/\text{kg}} = 60 \, \text{kg}$

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PISA-Type Question:

The farmer decides to split the parallelogram plot into two equal triangular sections by drawing a diagonal. What is the area of each triangular section?

Solution:
The area of each triangle is half the area of the parallelogram:
$\text{Area of one triangle} = \frac{A}{2} = \frac{6000}{2} = 3000 \, \text{m}^2$

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Follow-Up Questions:

1. If the cost of fencing is $5 per meter, what is the total cost?
2. If the farmer sells the land for $20 per square meter, how much money does he earn?
3. What happens to the perimeter if the base and side lengths are doubled?
4. How does the area change if the height of the parallelogram is increased by 20%?
5. If the parallelogram's angles are not right angles, how does this affect the height?

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Tip:

To solve parallelogram problems, remember that the height is always perpendicular to the base, and the area formula remains valid regardless of the shape of the angles.