"| |" never means "square root". It means absolute value if it is around a number, length if it is around a vector. Of course, you then use the square root to find the length of the vector (and to find an absolute value: ) but it is incorrect to say that it means square root!
By the way, this is NOT a right triangle but, fortunately, the area of any triangle, "right" or not, with two sides formed by vectors and is . There the | | clearly means "length" (or "magnitude") because is a vector.