The perimeter of the rhombus is 40 and one of the corners is 45 degrees. Find the area of a rhombus divided by √ 2

univerkov | July 2, 2021 | education

Since a rhombus has the lengths of all its sides are equal, then Ravsd = 4 * AB.

AB = Ravsd / 4 = 40/4 = 10 cm.

AB = BC = CD = AD = 10 cm.

Determine the area of the rhombus: Sravsd = AB * AD * Sin45 = 10 * 10 * √2 / 2 = 50 * √2 cm2.

Then Savsd / √2 = 50 * √2 / √2 = 50 cm2.

Answer: Savsd / √2 = 50 cm2.

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