refer to a seven piece tangram:
a. if the original square made by the seven tangram pieces has an edge length of 2, what are the edge lengths of the small square piece?
b.the parallelogram is what percent of the original square made by the seven tangram peieces?
c. if the largest triangle is "X" and the smallesr triangle is "Y", find the following:
I. 1/2X (divided by) Y
II. 2Y+3/4X
III. 3Y (divided by )X
To answer these questions about the seven-piece tangram, we need to understand the shapes involved and their relationships. Let's start by analyzing the seven pieces and their characteristics.
The seven tangram pieces consist of one large triangle (called "X"), one medium-sized square, one small square, and four other small triangles (two identical medium-sized triangles and two identical small triangles). The goal is to arrange these pieces to form a large square.
a. To determine the edge lengths of the small square piece, we need to examine the relationships between the different pieces. Since the original square made by the tangram pieces has an edge length of 2, we can deduce the following:
- The large triangle (X) forms half of the original square's area. Therefore, its area is 2*2/2 = 2 square units.
- The medium-sized square piece has an area equal to the difference between the area of the large triangle and the original square. So, its area is 2 - 2 = 0 square units.
- The small square piece makes up the difference in area between the medium-sized square and the original square. Therefore, its area is 2 - 0 = 2 square units.
- Since the area of a square is equal to the side length squared, we can find the side length of the small square by taking the square root of its area. Thus, the edge length of the small square piece is √2, approximately 1.41 units.
b. To find what percentage the parallelogram is of the original square, we need to determine its area. Let's call the parallelogram "P".
- The large triangle (X) occupies half of the original square's area, which is 2 square units.
- The medium-sized square occupies zero area, as discussed in part a.
- The remaining area of the original square is taken up by the three small triangles (two medium-sized triangles + two small triangles). Each small triangle has half the area of the medium-sized triangle.
- The area of one medium-sized triangle is half the area of the large triangle, so it's 2/2 = 1 square unit.
- Therefore, the area of two medium-sized triangles is 1 + 1 = 2 square units.
- The area of two small triangles is the same as the area of one medium-sized triangle, so it is also 1 square unit.
- To find the area of the parallelogram, P = Area of original square - Area of X - Area of small square - Area of small triangles.
- P = 2 - 2 - 0 - 2 - 1 = -3 square units.
Since the area cannot be negative, we can conclude that the parallelogram cannot be formed using the given seven tangram pieces. Therefore, we cannot determine its percent with respect to the original square made by the tangram pieces.
c. Now, let's find the values for the given expressions:
I. 1/2X (divided by) Y:
- "X" refers to the largest triangle. Its value is not specified, so we don't have enough information to evaluate the expression.
II. 2Y + 3/4X:
- "Y" represents the smallest triangle. Its value is not specified, so we don't have enough information to evaluate the expression.
III. 3Y (divided by) X:
- Again, since the values of "Y" and "X" are not given, we cannot determine the result of this expression.
In summary, without the specific values for "X" and "Y," we cannot calculate the results of the expressions in part c.