In parallelogram ABCD, the side AD is 12 cm and the angle BAD is 47 ° 50 ‘. Find the area of the parallelogram

In parallelogram ABCD, the side AD is 12 cm and the angle BAD is 47 ° 50 ‘. Find the area of the parallelogram if its diagonal BD is perpendicular to the AB side.

Consider a triangle ABD. (rectangular) Cos 47 * 50 ‘= AB / AD => AB = 12 * (cos 47 * 50’) Sin 47 * 50 ‘= BD / AD => BD = 12 * (sin 47 * 50’) Since cos 47 * 50 ‘and sin 47 * 50’ are not tabular numbers, so we write them down. AB- side AD- height S = AB * AD => S = 12 * (cos 47 * 50 ‘) * 12 * (sin 47 * 50’) = 144 * Sin (95 * 40 ‘) / 2 => S = 72 * Sin (95 * 40 ‘)