The diagonal of a parallelogram is equal to its side. Find the area of the parallelogram if one

| May 14, 2021 | education

The diagonal of a parallelogram is equal to its side. Find the area of the parallelogram if one of its sides is 14 cm and one of the corners is 60 degrees?

1) A parallelogram is a quadrilateral in which opposite sides are pairwise parallel (lie on parallel lines).

2) First, consider the triangle ABD: From the condition we know that the angle BAD = 60, sides AB = BD = 14 cm, since the condition says that the diagonal is equal to the side, so we can conclude that the triangle ABD is isosceles. By the property of an isosceles triangle, the angles at the base are equal, i.e. angle BAD = angle BDA = 60 degrees. You can find the third angle: ABD = 180 – (60 + 60) = 60. All three angles are equal to 60 degrees, so the triangle is also equilateral, AB = BD = AD = 14 cm.

3) Area of ​​a parallelogram ABCD = 1/2 * AB * AD * sin BAD = 1/2 * 14 * 14 * (√3) / 2 = 98√3 (cm ^ 2).



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