Find the side and area of the rhombus if its diagonals are 10cm and 24cm.

Before writing the solution, I want to say that in this problem there are two ways to find the area. I will analyze both options.
First, let’s find a side. As you know, the diagonals of a rhombus are divided by the intersection point in half (like a square, rectangle, etc.). Take separately one small right-angled triangle in which the legs are 5 and 12, respectively. Now, by the Pythagorean theorem, we find the hypotenuse (it will be the side of the rhombus). It will be 13.
Now we are looking for the area of ​​the rhombus. Option one:
S = d1d2 / 2 = 10 * 24/2 = 120
the second way: the rhombus consists of 4 small rectangular squares. Find the area of ​​one and multiply by 4.
S = 1 / 2ah = 1 \ 2 * 5 * 12 = 30
30 * 4 = 120
Answer: the side of the rhombus is 13, the area of ​​the rhombus is 120