A geometric solution to the problem. Assume each brick is one unit by one unit. This is the tricky part, because the original bricks were not drawn to look like squares. This simplification makes the area of the bricks equal to the number of the bricks. Find the area of the triangle and you've found the number of bricks!

The total area is found by adding the area inside the triangle to the area outside the triangle.

Total area = area inside + area outside.

The area of the triangle inside the edges is found using the formula for the area of a triangle area = base * height. This gives us ½*50*50=1250. The part hanging over the edge of the triangle has an area of .25 units squared. There are 100 total of these pieces. Each piece is ¼ unit squared, so 100*1/4=100/4=50/2=25. So the area of the bricks is 1250+25=1275.

Generalizing we find that ½*n*n+n/2=n(n+1)/2=sum of the first n integers.