Area of a square from its diagonal:\nFind the area (in sq. m) of a square whose diagonal measures 3.8 m.

Difficulty: Easy

Correct Answer: 7.22 sq.m

Explanation:


Introduction / Context:
For a square of side s and diagonal d, the relation is d = s√2. Hence the area s^2 can be written in terms of d as s^2 = d^2 / 2.


Given Data / Assumptions:

  • Diagonal d = 3.8 m.
  • Area A = s^2 = d^2 / 2.


Concept / Approach:
Compute d^2 and divide by 2 to get area. Keep two decimal places to match options.


Step-by-Step Solution:

d^2 = (3.8)^2 = 14.44.A = d^2 / 2 = 14.44 / 2 = 7.22 sq. m.


Verification / Alternative check:

Alternatively, s = d/√2 ≈ 3.8 / 1.4142 ≈ 2.687; s^2 ≈ 7.22 sq. m.


Why Other Options Are Wrong:

4.22, 5.22, 6.22 come from dividing by larger numbers than 2 or mis-squaring 3.8.


Common Pitfalls:

Using area = d^2 (forgets the /2 factor) or treating diagonal as side.


Final Answer:

7.22 sq.m

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