Find the area of a square if one of its diagonals is 3.8 m long. What is the area of the square (in sq m)?

Introduction / Context:This question tests the relationship between the diagonal of a square and its area. In a square, the diagonal forms a right triangle with two equal sides. By the Pythagoras relationship, diagonal = side*sqrt(2). Once the side length is expressed in terms of the diagonal, area is side^2. A very efficient identity is: area of a square = (diagonal^2) / 2. Using this avoids calculating sqrt(2) explicitly and reduces rounding errors. Units must be handled carefully: diagonal is in metres, so area will be in square metres.

Given Data / Assumptions:

• Diagonal d = 3.8 m
• For a square: d = s*sqrt(2)
• Area A = s^2

Concept / Approach:Use A = d^2 / 2. Compute 3.8^2, divide by 2, and keep the result in sq m.

Step-by-Step Solution: A = d^2 / 2 d^2 = 3.8 * 3.8 = 14.44 A = 14.44 / 2 = 7.22

Verification / Alternative check:Compute side explicitly: s = 3.8 / sqrt(2). Then area s^2 = (3.8^2)/(2) = 7.22, which matches the direct method and confirms correctness.

Why Other Options Are Wrong: 6.22 and 8.22 come from incorrect squaring or division. 4.22 and 3.22 result from using d/2 as side or other wrong diagonal-side relations.

Common Pitfalls:Treating diagonal as a side, forgetting to square, or dividing by sqrt(2) incorrectly and introducing rounding errors too early.

Final Answer:The area of the square is 7.22 sq m.