The rhombus side ABCD is 22 and the angle A is 45 degrees. Find the area of the rhombus.

univerkov | April 26, 2021 | education

Let’s draw the height from the vertex D to the side AB. In triangle АНD, the angle НD is straight, and the angle НAD is 45, then the angle АDН = 180 – 90 – 45 = 45, and therefore the triangle АНD is isosceles and АН = DH.

Then НD / АD = Sin45.

НD = АD * Sin45 = 22 * √2 / 2 = 11 * √2.

Then Savsd = AB * HD = 22 * 11 * √2 = = 242 * √2.

Answer: The area of the rhombus is 242 * √2 cm2.

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