Yes, my inspiration was the 19th century tangram puzzle, which had 7 pieces called tans.I too have memories of playing that in my childhood, it used to be fun. Netflix has a game called shapes that is exactly Tangram but web based

It is meant to promote thinking in simple shapes. A basic design practice to break complex items down to simpler shapes.

And no, it's not possible to resize the shapes. You are supposed to fill the silhouette using available shapes only.

I guess what you are referring to is that you might be seeing a triangle spot but the triangle you have is smaller. You are supposed to join two triangles in a way that makes a bigger triangle. Two triangles and a square if arranged properly can make a even bigger triangle.