The base of a parallelogram is twice its height. If the area of the parallelogram is 338 square centimetres, find the height of the parallelogram in centimetres.

Introduction / Context:
This question involves the area formula for a parallelogram and a simple algebraic relationship between base and height. The base is given as twice the height, and the area is known. By expressing the base in terms of height, we can form an equation and solve for the height. Such problems reinforce the connection between geometry and basic algebra.

Given Data / Assumptions:

• Let height of the parallelogram = h cm.
• Base of the parallelogram = 2h cm (twice the height).
• Area of the parallelogram A = 338 sq cm.
• Area formula: A = base * height.

Concept / Approach:
The area of a parallelogram is given by the product of its base and height. Here, both base and height are expressed in terms of h. Substituting into the area formula, we get a simple quadratic equation in h. Solving this equation by taking a square root gives the height. Since height is a length, we take the positive root only.

Step-by-Step Solution:
Let height = h cm. Then base = 2h cm.Area A = base * height = 2h * h = 2h^2.Given A = 338 sq cm, so 2h^2 = 338.Divide both sides by 2: h^2 = 338 / 2 = 169.Therefore h = sqrt(169) = 13 cm (taking the positive value).Thus, the height of the parallelogram is 13 cm.

Verification / Alternative check:
With height h = 13 cm, base = 2h = 26 cm. Area = base * height = 26 * 13. Compute 26 * 13 = (20 * 13) + (6 * 13) = 260 + 78 = 338 sq cm, which matches the given area. This confirms that the height of 13 cm is consistent with all the data in the question.

Why Other Options Are Wrong:
If h = 14 cm, base would be 28 cm and area = 28 * 14 = 392 sq cm, too large. If h = 16 cm, area would be 32 * 16 = 512 sq cm. A height of 12 cm would give area 24 * 12 = 288 sq cm, which is too small. A height of 18 cm gives 36 * 18 = 648 sq cm. None of these areas equal 338 sq cm, so these options are incorrect.

Common Pitfalls:
A common mistake is to add base and height instead of multiplying them, or to misinterpret the phrase base is twice the height. Some learners also forget to divide by 2 when solving 2h^2 = 338, resulting in an incorrect value for h^2. Always write down the area formula clearly, substitute, simplify, and then take the square root carefully to avoid these errors.

Final Answer:
13 cm