Find the side and area of the rhombus if its side is 10 cm and 24 cm.

The diagonals of the rhombus are perpendicular to each other, forming four identical right-angled triangles inside the rhombus. The intersection of the diagonals divides each one in half. Half of each diagonal is the legs of any given right-angled triangle. Let’s find these legs a and b:

a = 10/2 = 5 cm;

b = 24/2 = 12 cm;

Now, by the Pythagorean theorem, we find the hypotenuse of a right-angled triangle with, which is the side of the rhombus:

c² = 5² + 12²;

c = 13 cm – side of the rhombus.

The area of the rhombus is equal to the half-product of the diagonals:

S = (10 + 24) / 2 = 17 cm² – area of a rhombus.