# In a parallelogram, the sides are 4 and 6 cm, and the acute angle is 45. Find its smaller diagonal.

July 28, 2021 | education

| A parallelogram is a quadrilateral in which opposite sides are equal and lie on parallel lines.

In order to calculate the length of the smaller diagonal of the parallelogram, we use the formula for the length of the diagonal behind the sides and the angle between them:

d = √a ^ 2 + b ^ 2 – 2ab cosα, where:

d – smaller diagonal;

a, b – sides of the parallelogram;

α is an acute angle of a parallelogram.

cos 45 ° = √2 / 2 ≈ 0.525;

d = √ (4 ^ 2 + 6 ^ 2 – 2 ∙ 4 ∙ 6 ∙ √2 / 2) = √ (16 + 36 – 48 ∙ 0.525) = √ (52 – 25.2) = √26.8 ≈ 5 , 18 cm.

Answer: The length of the smaller diagonal is 5.18 cm.

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