A parallelogram has a base that is twice its height. If the area of the parallelogram is 72 sq cm, find the height of the parallelogram in cm, keeping the “base is twice the height” condition unchanged.

Introduction / Context:
This is a basic mensuration question about the area of a parallelogram. The formula is area = base * height. Since the base is related to the height (base = 2 * height), you substitute this relationship into the area formula and solve a simple quadratic equation for the height.

Given Data / Assumptions:

• Area of parallelogram = 72 sq cm
• Base b is twice the height h, so b = 2h
• Area formula: A = b * h

Concept / Approach:
Substitute b = 2h into A = b * h to get A = 2h^2. Solve for h using the given area value 72.

Step-by-Step Solution:

Verification / Alternative check:
If h = 6, then base b = 2 * 6 = 12. Area = 12 * 6 = 72 sq cm, exactly matching the given area. So the computed height is correct.

Why Other Options Are Wrong:

Common Pitfalls:
Students sometimes use the triangle area formula 1/2 * base * height by mistake. Another common error is taking h = 36 instead of sqrt(36). Always remember that h^2 = 36 implies h = 6, not 36.

Final Answer:
6 cm