The side of the rhombus is 50 cm. And the diagonal is 80 cm. Find the area of the rhombus.

Rhombus side (a) = 50 cm;
Diagonal of a rhombus (d) = 80 cm;
Sр -? cm ^ 2.
The area of a rhombus is calculated by the formula: Sр = 1/2 * d1 * d2, i.e. Sp = 1/2 * AC * BD;
From the triangle ABO (rectangle) according to Comrade Pythagoras we find the ВO:
BO = √ (AB ^ 2 – AO ^ 2);
In a rhombus, the diagonals are divided in half by the intersection point, which means AO = AC: 2 = 80: 2 = 40 (cm);
ВO = √ (50 ^ 2 – 40 ^ 2) = √ (2500 – 1600) = √ (900) = 30 (cm).
BD = BO * 2 = 30 * 2 = 60 (cm);
Sp = 1/2 * 80 * 60 = 4800: 2 = 2400 (cm ^ 2).
Answer: the area of the rhombus is 2400 cm ^ 2.