Calculate the area and side of the square if the diagonal of the square is 12√2 m.

The diagonal of the square divides it into 2 equal, right-angled, isosceles triangles. Those. the diagonal of the square is the hypotenuse of these triangles. The side of a square (or the leg of a triangle) can be calculated using the sine theorem. Let’s say we have a square ABCD and a right-angled triangle ABC. AC diagonal. AC = 12√2, angle ABC = 90 degrees, angle BAC = BCA = 45 degrees => AC / sinB = AB / sinC, hence AB AB = AC * sinC / sinB = 12√2 * (√2 / 2) / 1 = 12m. The side of the square is 12 m.Square = 12 * 12 = 144m ^ 2.