The side of the rhombus is 26 and the diagonal is 48. Find the area of the rhombus.

Given: ABCD – rhombus, AC, BB – diagonals, AC = 48, BC = 26.

Find: SABCD -?

Decision:

The area of a rhombus is calculated by the formula: SABCD = 1/2 * d1 * d2, where d1, d2 are the diagonals of the rhombus.

Let O be the intersection point of the diagonals of the rhombus. Consider ∆ BOC: ∠ BOC = 90о, because the diagonals of the rhombus intersect at an angle of 90o. By the Pythagorean theorem, we find the OS:

OS ^ 2 = ВС ^ 2 – ОВ ^ 2, while ОВ = 1/2 ВD = 24;

OS ^ 2 = 676 – 576 = 100;

OS = √100 = 10;

Hence, AC = 2 OC = 20;

S = 1/2 * AC * BD = 1/2 * 20 * 48 = 480.

Answer: 480