Find the area of a regular triangle whose side is equal to the side of the rhombus with diagonals 10 and 12.

The intersection point of the diagonals of the rhombus divides the diagonals in half and forms four identical right-angled triangles in the rhombus, in which the side of the rhombus is the hypotenuse. Divide the diagonals of the rhombus in half and get the legs of a right-angled triangle 5 cm and 6 cm.Now we find the side of the rhombus by the Pythagorean theorem:

c² = a² + b²;

c² = 5² + 6²;

c² = 25 + 36;

c² = 61;

c = √61 cm.

Now we find the area of a regular triangle with a side of √61 cm:

S = a²√3 / 4;

S = √61√3 / 4;

S = √64 / 4;

S = 8 * 4;

S = 32 cm².