Geometry and Trigonometry practice question

Answer: 50

The diagonal splits the square into two right triangles with legs s: s² + s² = 100, so 2s² = 100 and s² = 50. The area is s² = 50. (Or: a square's area is half the square of its diagonal.)

Common wrong answers

If you answered 25

25 is (10/2)². Halving the diagonal doesn't give the side; the side is 10/√2 ≈ 7.07.

If you answered 40

40 is 4 × 10, treating the diagonal as a side and finding a perimeter.

If you answered 100

100 is the diagonal squared — that is 2s², twice the area.

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