The trapezoid has a diagonal of 8 cm and a 5√3a angle between them – 30 degrees. Find the area of the trapezoid.

In the ABCD trapezoid, the AC diagonal = 8 cm; diagonal B = 5 cm; О is the point of intersection of the diagonals; angle BOA = 30 °;

The formula for calculating the area of a trapezoid from the known diagonals and the angle between them:

S = 0.5 * AC * BD * sin <BOA;

sin 30 ° = 0.5;

S = 0.5 * 8 * 5 * 0.5 = 10 (cm²).