Question 1179494: Think of the area of the entire tangram shape as equal to 1 square unit. What are the area measurements of each fractional piece?
Answer by greenestamps(13200)   (Show Source):
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(1) The two largest triangles cover half of the whole square; the area of each of them is half of the area of half of the whole square: half of a half of 1 is 1/4.
(2) The remaining 5 pieces cover the other half of the whole square; the sum of their areas is 1/2.
Let the area of each of the smallest triangles be x; then picture cutting up the remaining pieces into pieces the size and shape of that smallest triangle.
(a) the area of each of the two smallest triangles is x
(b) the area of the middle size triangle is 2x
(c) the area of the square is also 2x
(d) the area of the parallelogram is also 2x
The total area of those pieces is 8x; since together they cover half of the whole square, x is one-eighth of one half, or 1/16.
ANSWERS:
each large triangle: area 1/4
middle size triangle, square, and parallelogram: area 2x=2/16=1/8 each
smallest triangles: x=1/16 each
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