The diagonal of a square is 10 cm. Find its area.

Explanation

• For a square, area = d²/2, so the area is 10²/2 = 100/2 = 50 cm².
• The longer route gives the same result: side = d/√2 = 10/√2, and squaring that leaves 100/2 = 50 cm².
• Option D 100 cm² treats the diagonal as though it were the side of the square.
• The side here is about 7.07 cm, so an area close to 50 cm² is what you should expect.
• The formula comes from the diagonal cutting the square into two right-angled triangles, with the sides as the legs.