Find the area of a rhombus with a side of 12 cm if its large diagonal = 14 cm.

It is known that the diagonals of a rhombus intersect at right angles and are halved at the point of intersection. For a right-angled triangle formed by half the diagonals and the side of a rhombus, according to the Pythagorean theorem, you can write:

d1 ^ 2 + d2 ^ 2 = a ^ 2;

d2 ^ 2 = a ^ 2 – d1 ^ 2 = 12 ^ 2 – 7 ^ 2 = 144 – 49 = 95;

d ^ 2 = √95 – half of the smaller diagonal.

The area of a rhombus can be found as half the product of the lengths of its diagonals:

S = D1 * D2 / 2 = D1 * 2 * d2 / 2 = D1 * d2 = 14√95 ≈ 136.46 cm2.