Find the area and perimeter of a square whose length of diagonals is 20$\sqrt2$ cm.

Analyze the question: We are given the diagonal of a square, d = 20√2 cm. We need the area and the perimeter.

Concept: For a square with side s, the diagonal is d = s√2 (from Pythagoras: d² = s² + s² = 2s²).

Also, Area = s² and Perimeter = 4s.

Solution:

1. Find the side: s√2 = 20√2 s = 20 cm

2. Area: A = s² = 20² = 400 cm²

3. Perimeter: P = 4s = 4 × 20 = 80 cm

(Check using the diagonal formula: Area = d²/2 = (20√2)²/2 = 800/2 = 400 cm². ✓)

Checking the options:

• A: 800 cm², 80 cm. The area is wrong (800 is d², not d²/2).
• B: Has the units swapped (area in cm, perimeter in cm²), so it is wrong.
• C: Also has the units swapped and the values reversed, so it is wrong.
• D: 400 cm², 80 cm. This matches our working.

Tip: For a square, Area = d²/2. This is a quick shortcut when the diagonal is given. Be careful with option A: it is a trap for students who forget to divide d² by 2. Also check the units: area must be in cm² and perimeter in cm.