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

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

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

Angle A = 60 °, AB = 5 cm.

In a right-angled triangle ABH, the angle ABH = 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 right-angled triangles НBD, according to the Pythagorean theorem, determine the length of the leg НD.

НD ^ 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