A tangram is a geometric puzzle made from seven pieces
that form a square. Trace the pieces, cut them out, and
answer the following questions. The puzzle can also be seen on wikipedia web site.
a. If the area of the entire square equals 1 unit, label
each piece with its rational number area.
Here is what I have and I gave each a letter to identify it:
Triangles:
2 small triangles c,e
1 medium triangle g
2 large triangles a,b
Square d
Parallelogram f
The rational number area is-
Letter a 1/4
B 1/4
C 1/16
D 1/8
E 1/16
F 1/8
G 1/8
All together this totals 1
Is this right?
Yes, your rational number areas for each piece of the tangram are correct. The area of the entire square is 1 unit, and when you add up the areas for each piece (1/4 + 1/4 + 1/16 + 1/8 + 1/16 + 1/8 + 1/8), the total is indeed 1. Well done!
Yes, your rational number areas are correct. To confirm this, we can calculate the area of each shape and add them up.
Triangle c and e (small triangles): Since each small triangle has half the area of the medium triangle, and the medium triangle has 1/8 of the area of the square, each small triangle has an area of (1/8) * (1/2) = 1/16.
Triangle g (medium triangle): This triangle has an area of 1/8 of the square.
Triangles a and b (large triangles): Each large triangle has double the area of the medium triangle, so each has an area of (1/8) * 2 = 1/4.
Square d: This square has an area of 1/4.
Parallelogram f: This parallelogram has the same area as one large triangle, which is 1/4.
Adding up the areas:
(1/4) + (1/4) + (1/16) + (1/8) + (1/16) + (1/8) + (1/8) = 1
So, your total area adds up to 1, which means your assigned rational number areas are correct.