Find the area of a square, one of whose diagonals is 4.8 m long.

Correct — D. The four options are images, reading 12.5 m², 10.5 m², 9.5 m² and 11.52 m².

Rule: for a square of diagonal d, area = d² ⁄ 2. (The diagonal is a√2, so d² = 2a², and a² = d² ⁄ 2.)

Square the diagonal:
4.8² = 23.04

Halve it:
23.04 ÷ 2 = 11.52 m² → option (d), the image reading 11.52 m².

Why the others are wrong

• (a)
  12.5 is d² ⁄ 2 with the diagonal rounded up to 5. Squaring magnifies the rounding: 4.8² is 23.04, not 25, and the 0.2 m you discarded costs nearly a whole square metre.
• (b)
  10.5 would need a diagonal of √21 ≈ 4.58 m. The given diagonal is 4.8 m, and the only halved square available is 23.04 ÷ 2.
• (c)
  9.5 would need a diagonal of about 4.36 m. Note that the side route agrees with the diagonal route: a = 4.8 ⁄ √2 ≈ 3.394 m, and 3.394² ≈ 11.52.

A square has two routes from the diagonal to the area, and they must agree.

The long way: the diagonal splits the square into two right isosceles triangles, so d = a√2, giving a = d ⁄ √2, and then area = a².

The short way: square the diagonal and halve it, area = d² ⁄ 2.

The same formula arrives from a different direction — a square is a rhombus whose diagonals are equal, and a rhombus has area d₁d₂ ⁄ 2, which becomes d² ⁄ 2.

Key facts

• For a square of side a, the diagonal is a√2.
• Area of a square from its diagonal is d² ⁄ 2.
• A rhombus has area d₁d₂ ⁄ 2, and a square is the case d₁ = d₂.
• 4.8² = 23.04, and half of 23.04 is 11.52.

Common traps

• Halving the diagonal before squaring it instead of after
• Stopping at d² and forgetting to divide by 2
• Rounding 4.8 to 5 to make the squaring easier

No directly related past PYQ was found.