The parallelogram angle is 60 degrees, the smaller diagonal is 7cm

| April 1, 2021 | education

The parallelogram angle is 60 degrees, the smaller diagonal is 7cm, and one of the sides is 5cm. Find the area and perimeter of the parallelogram.

From the top B let us lower the height BH to the base of AD.

In a right-angled triangle ABН, the angle ABН = 180 – 60 = 30, then the leg AH is equal to half the length of the hypotenuse AB. AH = 5/2 = 2.5 cm.

Then the height of BH, according to the Pythagorean theorem, will be equal to: BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 6.25 = 18.75.

From the right-angled triangles НВD, according to the Pythagorean theorem, determine the length of the leg НD.

HD ^ 2 = BD ^ 2 – BH ^ 2 = 49 – 18.75 = 30.25.

НD = √30.25 = 5.5 cm.

Then the side AD = AH + HD = 2.5 + 5.5 = 8 cm.

Determine the perimeter of the parallelogram.

P = 2 * (AB + AD) = 2 * (5 + 8) = 26 cm.

Determine the area of ​​the parallelogram.

S = AD * BH = 8 * √18.75 = 34.6 cm2.

Answer: The perimeter is 26 cm, the area is 34.6 cm2.



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