First, let's find the area of the shaded parts. Since the shaded squares and triangles are the same size, then all shaded squares have sides 3 in. by 3 in. because the shaded square in the middle has sides 3 in. by 3 in.
We can also see that the shaded triangles have legs 6 in. and 6 in. because one of the shaded triangles in the figure are labeled 6 in by 6 in.
Now we can find the area of the shaded square and triangle (area of a square is side^2 while the area of a triangle is base*height/2).
Shaded Square Area: 3^2 = 9 in^2
Shaded Triangle Area: 6*6/2 = 18 in^2
There are 5 shaded squares and 4 shaded triangles, so we can determine the shaded area now:
Shaded Area: 9*5 + 18*4 = 45 + 72 = 117 in^2
Now we need to find the area of the white rectangles and the area of the white triangles. We can see that the sides of the white rectangles are 6 in. and 3 in. We can also see that the sides of the white triangles are 3 in and 3 in.
Now we can find the area of the white rectangle and the white triangle.
White Triangle Area: 3*3/2 = 9/2 = 4.5 in^2
White Rectangle Area: 3*6 = 18 in^2
There are 4 white rectangles and 8 white triangles, so we can determine the white area now:
White Area: 4*18 + 8*4.5 = 72 + 36 = 108 in^2
The ratio of the area of the shaded pieces to the area of the white pieces is 117/108.
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