Rectangles & Parallelograms – Base twice the height:\nThe base of a parallelogram is exactly twice its height. If the area of the parallelogram is given as 338 sq cm, determine the height (in cm). Keep units standardised and show the core relation area = base * height.

Introduction / Context:
Questions on parallelograms typically use the direct formula Area = base * height. When one dimension is a multiple of the other, the unknown can be found using a single algebraic equation.

Given Data / Assumptions:

• Area = 338 sq cm.
• Base = 2 * height.
• All measurements are in centimetres.

Concept / Approach:
Let height = h. Then base = 2h. Area formula becomes 2h * h = 2h^2. Solve for h from 2h^2 = 338.

Step-by-Step Solution:

Verification / Alternative check:
Base = 2 * 13 = 26 cm; Area check: 26 * 13 = 338 sq cm ✔️

Why Other Options Are Wrong:
14 cm ⇒ area 28*14 = 392 (too high); 16 cm ⇒ 32*16 = 512; 12 cm ⇒ 24*12 = 288; 'None' is unnecessary as an exact match exists.

Common Pitfalls:
Confusing base with height or using perimeter ideas instead of area; forgetting that only the positive root is physically meaningful.

Final Answer:
13 cm