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

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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

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

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