The smaller diagonal of the rhombus is 10 cm and is equal to its side. Find the area of the rhombus.

The diagonals of the rhombus are mutually perpendicular. The area of a rhombus along the diagonals is half the product of the diagonals (S = (d1 * d2) / 2). Since the diagonals at the intersection form 4 right-angled triangles, we can use the Pythagorean theorem. Also, the diagonals of the rhombus are bisected by the point of intersection. That is, one of the legs is 5 (10: 2 = 5)
by c. Pythagoras: x ^ 2 + 25 = 100; x ^ 2 = 75 x = 5√5. This is half of the second diagonal
S = (2 * 5√5 * 10) / 2 = 50√5