Understanding the Problem
To find the area of a parallelogram, we need to know the height and the length of the base. In this case, we have:
- The distance between the parallel sides (height) = 2 cm
- The sum of the lengths of the parallel sides = 10 cm
Finding the Base Length
Since the sum of the lengths of the two parallel sides is 10 cm, we can denote them as 'a' and 'b':
- a + b = 10 cm
However, for calculating the area, we can use the average of the two sides as the base.
Calculating the Average Base Length
The average length of the bases can be calculated as:
- Average base length = (a + b) / 2
- Average base length = 10 cm / 2 = 5 cm
Calculating the Area
The formula for the area of a parallelogram is:
- Area = Base × Height
Now substituting the values we have:
- Area = Average base length × Height
- Area = 5 cm × 2 cm
Final Calculation
- Area = 10 cm²
Conclusion
The area of the parallelogram with parallel sides that are 2 cm apart and whose lengths sum to 10 cm is:
- 10 cm²
This method shows how important it is to utilize both the height and the average base length to find the area effectively.

Area = 6cm²