What fraction of the area of the square is each of these triangles?
For the small square, I looked at each of the 4 triangles:
1. For the smallest triangle in the corner, it's 1/8 because I know that 2 together will make 1/4, so in all there are 4 x 2 = 8 of these small triangles in the whole.
2. For the two right triangles along the sides, it's 1/4 because if I put two together, that will make 1/2 of the whole, so 4 of these triangles would cover the whole.
3. For the big middle triangle, I added all the fractions of the other triangles:
1/4 + 1/4 + 1/8 = 5/8. Then I did 1 whole - 5/8 = 3/8. So, the area of the middle triangle is 3/8.
How is this made using the first square?
We multiplied the first square 4 times. The first square is 1/4 of the big square.
What is the shape that has been created in the middle of this larger square?
The shape in the middle is a rhombus.
What fraction of the total area of the large square does this shape take up?
We know that the rhombus is made up of 4 of the right triangles of the small square. There are 4 right triangles in the small square. Because there are 4 small squares in the big square, I do 4 x 4 = 16 right triangles in the big square. So, each right triangle is 1/16 of the big square. Since there are 4 right triangles in the rhombus, we have 4/16 for the area of the rhombus. 4/16 = 1/4, so the rhombus is 1/4 of the big square.