The base of a parallelogram is twice its height. If the area of the parallelogram is 72 square centimetres (cm^2), find its height in centimetres.

Introduction / Context:
This problem tests the basic area formula of a parallelogram: area = base * height. When a relationship between base and height is given (here base is twice the height), you can substitute that relationship into the area formula and solve for the height directly.

Given Data / Assumptions:

• Area A = 72 cm^2
• Base b = 2h, where h is the height
• Area of parallelogram = b * h

Concept / Approach:
Substitute b = 2h into A = b*h. This gives A = 2h^2, which can be solved by simple algebra to find h.

Step-by-Step Solution:
A = b*h 72 = (2h)*h 72 = 2h^2 h^2 = 72/2 = 36 h = sqrt(36) = 6 cm

Verification / Alternative check:
If height is 6 cm, then base = 2*6 = 12 cm. Area = 12*6 = 72 cm^2, matching the given area.

Why Other Options Are Wrong:
3 cm: would give base 6 cm, area 18 cm^2. 4 cm: would give base 8 cm, area 32 cm^2. 8 cm: would give base 16 cm, area 128 cm^2. 12 cm: would give base 24 cm, area 288 cm^2.

Common Pitfalls:
Using triangle formula (1/2*b*h) by mistake. Forgetting that base is twice height and swapping them. Making an error when taking square root.

Final Answer:
Height = 6 cm