Diagonal BD of parallelogram ABCD is perpendicular to side AD. Find the area of the parallelogram ABCD

univerkov | May 20, 2021 | education

Diagonal BD of parallelogram ABCD is perpendicular to side AD. Find the area of the parallelogram ABCD if AB = 12 cm, angle A = 41 °.

In a right-angled triangle ABD we find leg BD, through sin A, and leg AD through cos A.
BD = sin A * AB = sin 41 ° * 12 = 0.65 * 12 = 7.8 cm.
AD = cos A * AB = cos 41 ° * 12 = 0.75 * 12 = 9 cm.
S ABCD = BD * AD = 7.8 * 9 = 70.2 cm²
Answer: ABCD area 70.2 cm²

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