Question 328030: I really need help with this problem I do not understand it at all if any one can please help me I would greatly appreciate it thanks ahead of time.
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.
a. If the area of the entire square equals 1 unit, label
each piece with its rational number area.
b. If the area of piece (a) equals 1 unit, label each piece
with its rational number area.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
A tangram consists of the following pieces, with side measurements in proportion to the total square with side measurement of 1 unit.
5 right triangles
 2 small (hypotenuse of  and sides of  )
1 medium (hypotenuse of  and sides of )
2 large (hypotenuse of  and sides of )
1 square (side of )
1 parallelogram (sides of and )
So the area of an isosceles right triangle is side squared divided by 2. For example, the area of the small triangle is 
Use the dimensions above to calculate the area of the other two size triangles.
The area of the square is simply the measure of the side (given above) squared.
The parallelogram area is a little trickier. The short dimension is . If you draw in a height line perpendicular to the long side and passing through a vertex, then you form an isosceles right triangle with hypotenuse . Multiplied by is  , the measure of the altitude. Then the area of the parallelogram is just the altitude times the long side, which arithmetic you can do for yourself.
To check your work, add up all of the areas of all of the shapes. Since the large square has sides of 1 unit, the sum of the areas of the shapes must be 1 square unit.
As for the second part of the problem, you didn't happen to mention which of the shapes was shape (a). I'll just guess that it is the square. The square has an area of  of the overall square. Hence if you assign the value 1 to the area of the square, then the area of the overall square must be 8. Take each of the fractional areas calculated in the previous step and multiply by 8 to get the rational area of each of the other pieces in relation to the unit area assigned to the small square. If shape (a) is some other piece, use the denominator of its fractional area from the earlier part of the problem as the multiplier.
John
|
|
|
