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Learning Math Home
Measurement Session 6: Solutions
 
Session 6 Part A Part B Part C Homework
 
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A B C 
Homework

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Solutions for Session 6, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7


Problem C1

a. 

All sketches produce a similar triangle:

b. 

No, it is four times larger. In all cases, the area of a doubled polygon is four times the area of the original. Tripling the side lengths results in a polygon nine times larger in area. Quadrupling the side lengths results in a polygon 16 times larger in area -- and so on.

<< back to Problem C1


 

Problem C2

If Ao is the area of the original polygon, then we can write the following:

Polygon

Scale Factor of 2 -- Area of the Enlargement in Terms of the Original Shape

Scale Factor of 3 -- Area of the Enlargement in Terms of the Original Shape

Scale Factor of 4 -- Area of the Enlargement in Terms of the Original Shape

Rectangle C

4 • Ao

9 • Ao

16 • Ao

Parallelo-
gram M

4 • Ao

9 • Ao

16 • Ao

Trapezoid K

4 • Ao

9 • Ao

16 • Ao

<< back to Problem C2


 

Problem C3

The number of copies needed is the square of the scale factor. For example, making a copy that is three times larger in each direction will take nine copies of the original shape.

<< back to Problem C3


 

Problem C4

The area of the enlarged figure is the original area multiplied by the square of the scale factor.

<< back to Problem C4


 

Problem C5

Because the scale factor is 3, the area is nine times larger. Therefore, the area of the enlarged figure is 72 cm2.

For example, suppose the original figure were a 4-by-2 rectangle (with an area of 8 cm2). The new shape would then be 12 by 6, with an area of 72 cm2 -- nine times the original area. Here's how it breaks down:

A = 12 • 6
A = (4 • 3) • (2 • 3)
A = 4 • (3 • 2) • 3associative property
A = 4 • (2 • 3) • 3commutative property
A = (4 • 2) • (3 • 3) associative property

<< back to Problem C5


 

Problem C6

One way to think about it is that enlarging an object will require k copies of that object in each direction: k copies in one direction, multiplied by k copies in the other direction, for a total of k2.

<< back to Problem C6


 

Problem C7

All of these polygons are rep-tiles. Most rep-tiles have side lengths that have a common factor, but this is not a requirement.

<< back to Problem C7


 

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