The problem involves a parallelogram with a base of 6 units and a side length of 5 units. We are asked to find the corresponding height when the base is 6 units.

Looking at the diagram, there is a right triangle formed by the height (which is perpendicular to the base), one leg of 4 units, and the hypotenuse (side of the parallelogram) of 5 units. This suggests the use of the Pythagorean theorem.

Given:

• One leg = 4 units (height we need to find)
• Hypotenuse = 5 units (side of the parallelogram)
• Other leg is not relevant for this calculation.

Using the Pythagorean theorem: $\text{Hypotenuse}^2 = \text{Leg}_1^2 + \text{Leg}_2^2$ Substitute values: $5^2 = 4^2 + \text{height}^2$ $25 = 16 + \text{height}^2$ $\text{height}^2 = 25 - 16 = 9$ $\text{height} = \sqrt{9} = 3$

Thus, the height corresponding to the base of 6 units is 4 units.

The correct answer is C. 4 units.

Would you like more details or have any questions?

Here are 5 related questions:

1. How does the Pythagorean theorem apply to different shapes like triangles or parallelograms?
2. What are the other properties of a parallelogram?
3. How would the height change if the base length was increased?
4. Can the height of a parallelogram be greater than the side length?
5. How do we calculate the area of a parallelogram?

Tip: Always check for right triangles in geometric figures like parallelograms, as they often help in finding unknown lengths or heights.