In the parallelogram abcd, the angle a is 135 degrees, AB = root of 2 cm and AD = 8 cm.

In the parallelogram abcd, the angle a is 135 degrees, AB = root of 2 cm and AD = 8 cm. Calculate the area of the parallelogram

The first way.

Determine the magnitude of the acute angle of the parallelogram.

Angle ABC = 180 – 135 = 45.

Determine the area of the parallelogram.

Savsd = AB * BC * Sin45 = √2 * 8 * Sin45 = √2 * 8 * √2 / 2 = 8 cm2.

Second way.

Let’s draw the height of AН.

Angle ABC = 180 – 135 = 45, then the right-angled triangle ABН is isosceles, AB = BН.

Then Sin45 = AH / AB.

AH = √2 * √2 / 2 = 1 cm.

Determine the area of the parallelogram.

Savsd = AD * AН = 8 * 1 = 8 cm2.

Answer: The area of the parallelogram is 8 cm2.