Square — Perimeter 68 cm: Find the area (in square centimetres).

Difficulty: Easy

Correct Answer: 289 sq cm

Explanation:


Introduction / Context:
Given a square’s perimeter, the side is perimeter/4. Area is side^2. This item is a quick application of square properties and arithmetic squaring of an integer side length.



Given Data / Assumptions:

  • Perimeter P = 68 cm
  • Side s = P/4
  • Area A = s^2


Concept / Approach:
Compute the side, then square it to get the area. Keep units in centimetres squared for the final answer to match options exactly.



Step-by-Step Solution:

s = 68 / 4 = 17 cm.A = 17^2 = 289 cm^2.


Verification / Alternative check:

Reverse: A = 289 ⇒ s = 17 ⇒ P = 4 * 17 = 68 cm (consistent).


Why Other Options Are Wrong:

  • 361 and 324 are 19^2 and 18^2, not 17^2.
  • 284 and 269 are near misses from arithmetic errors.


Common Pitfalls:

  • Dividing by 2 instead of 4 to find the side.


Final Answer:
289 sq cm.

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