SOLUTION: The seven tangram pieces are arranged into the shape of a square with dimensions 1 unit by 1 unite. I need to determine the dimensions and area of each piece. So far I know the t

Question 924900: The seven tangram pieces are arranged into the shape of a square with dimensions 1 unit by 1 unite. I need to determine the dimensions and area of each piece. So far I know the two large isosceles right triangles have lengths of 1, square root 2/2, and square root 2/2. I can't assume any midpoints. I'm at a complete loss.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
place the arranged tangram pieces on a grid of squares ( 4 by 4) and each square has a side of 1/4 inch, now we calculate the hypotenuse of each square
(1/4)^2 + (1/4)^2 = h^2
1/16 + 1/16 = h^2
1/8 = h^2
h = sqrt(1/8) is approx 0.35 inch
now we can calculate the areas and dimensions of each tangram piece
Each of the large triangles has area 1/4 square inch ( A = (1/2)*1*(1/2))
The medium triangle has area 1/8 square inch (A = (1/2)*(1/2)*(1/2))
Each of the small triangles has area 1/16 square inch (A = (1/2)*(1/2)*(1/4))
The square has area .12 square inch (A = (.35)*(.35))
The parallelogram has area 1/8 square inch (A = (1/2) * (1/4))
I will leave the dimensions to you
as a check some the area
(1�4)+(1�4)+(1�8)+(1�16)+(1�16)+.12+(1�8) = 0.995
checks out

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