The length of the diagonal of a square is 12 cm. Calculate the area of the square.

Analyze the question: We're given the diagonal of a square (12 cm) and asked to find its area.

Concept: For a square with side s, the diagonal d forms the hypotenuse of a right-angled triangle with two sides of length s. By Pythagoras:

d² = s² + s² = 2s²

Since the area is A = s², we get:

A = d²/2

Solution:

Method 1 (using Pythagoras):

• 12² = 2s²
• 144 = 2s²
• s² = 72

Area = s² = 72 cm²

Method 2 (using the formula A = d²/2):

• A = 12²/2 = 144/2 = 72 cm²

(Equivalently, the side is s = 12/√2 = 6√2 cm, so the area is (6√2)² = 36 × 2 = 72 cm².)

Answer: The area is 72 cm², which is option C.

Tip: For any square, remember Area = (diagonal)² ÷ 2. This is also the rhombus formula (½ × d₁ × d₂) with both diagonals equal: ½ × 12 × 12 = 72. Option A (36) is the trap for students who forget to divide by 2 after squaring and instead compute something like 12 × 12 ÷ 4.