Isometric Areas
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Question: "Let's define a unit of area, T, such that the triangle has area 1T.
Here are some parallelograms whose side lengths are whole numbers.
*Refer To Picture*
Can you find the area, in terms of T, of each parallelogram?
Compare the results with the lengths of their edges."
A number of triangles in each parallelogram can be found by either counting by hand or by using a formula which will be covered later
Answers:
A: 16T
B: 24T
C: 24T
D: 4T
E: 16T
F: 18T
G: 8T
H: 12T
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Question: "What do you notice?
Can you explain what you've noticed?"
I found the formula out by guessing and checking.
Formula: T=2(B*H)
the number of triangles is equal to the base multiplied by the height of the parallelogram then multiplied by 2.
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Question: "Can you find a similar result for trapeziums in which all four lengths are whole numbers?"
Formula: H(A+B)
A stand for the top base and B stands for the bottom place. H stands for the height