The side of the diamond is 78 and the diagonal is 60. Find its area.

As you know, the diagonals of a rhombus are halved when they intersect.

And the halves of these diagonals, together with the side of the rhombus, form a triangle that is rectangular.

Therefore, first we determine what half of the diagonal known from the condition of our problem will be equal to:

60: 2 = 30.

Now, using the well-known formula from the Pythagorean theorem, we determine what half of the unknown diagonal is equal to:

√ (782 – 302) = √5184 = 72.

Then the diagonal is:

2 * 72 = 144.

Then the area is:

1/2 * 144 * 60 = 4320.

Answer: 4320.