In parallelogram ABCD, diagonal BD is perpendicular to side AB and equals 5 cm, AD = 8 cm

In parallelogram ABCD, diagonal BD is perpendicular to side AB and equals 5 cm, AD = 8 cm, angle A = 45 degrees. Find the area of the parallelogram.

Since, by condition, BD is perpendicular to AB, then the ABD triangle is rectangular, and since the angle BAD = 45, the triangle is also isosceles AB = BD.

Let’s draw the height BH of the triangle ABD, which will be the bisector and median of the triangle, then AH = DH = AD / 2 = 8/2 = 4 cm.

In a right-angled triangle ABН, the angle BAН = 45, then the triangle is isosceles and BH = AH = 4 cm.

Then the area of the parallelogram is equal to: Savsd = AD * BH = 8 * 4 = 32 cm2.

Answer: The area of the parallelogram is 32 cm2.