Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
December 18, 2015
8.3 Scale Diagrams
Learning Goals:
1.
Calculate scale factor
2.
Use scale factors to solve problems.
3.
Use scale factors to draw scale diagrams.
Oct 15­7:58 PM
Terminology:
Scale diagram: A drawing in which measurements are proportionally reduced or enlarged from actual measurements; a scale diagram is similar to the original.
Scale: The ratio of a measurement on a diagram to the corresponding distance measured on the actual object. The actual measurement is always written second. A scale always includes units, and they do not necessarily have to be the same.
Ex: on a map the scale may be written as 1cm:100km
Oct 15­7:58 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
December 18, 2015
Scale factor: A number created from the ratio of any two corresponding measurements of two similar shapes or objects. Scale factor can be written as a fraction, decimal, or percent. The actual measurement is always on the bottom of the fraction. The scale factor does not include units, because they are assumed to be the same.
Scale factor is represented by k:
If a scale factor is:
Less than 1 à the diagram is smaller than the actual object being represented
Greater than 1 à the diagram is larger than the actual object being represente
d
Oct 15­8:00 PM
Ex(1)
Determine the scale factor that was used to transform rectangle A into rectangle B
Oct 15­8:01 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(2)
December 18, 2015
A desk that is 150 cm long is drawn in a scale diagram as 15 cm long. What scale factor was used in the diagram?
Oct 15­8:06 PM
Ex(3)
A floor plan of a house was created using a scale of 2 cm: 1 m. What scale factor was used?
Oct 15­8:07 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(4)
December 18, 2015
A scale drawing uses a scale factor of 1/25. Is the drawing a reduction or an enlargement? If the length of the object in the drawing is 5 cm, what is the length of the actual object?
Oct 15­8:08 PM
You Try:
A scale diagram of an animal cell has a diameter of 3.5 cm. The actual cell has a diameter of 0.25 mm. What scale factor was used to create the diagram? Is this a reduction or enlargement?
Oct 15­8:08 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(5)
December 18, 2015
An 8 x 10 inch photograph is going to be used to create a display poster. The maximum allowable poster dimensions are 30 x 40 inches. What is the greatest scale factor that could be used to enlarge the original photo and still fit the maximum dimensions? What would the poster dimensions be after this enlargement?
Oct 15­8:09 PM
Ex(6)
To make a scale drawing of a rectangular park, a scale factor of 1/1000 or 0.001 is to be used. If the length and width of the park are 100 m and 75 m, how long would the length and width be in the scale drawing?
Oct 15­8:10 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(7)
December 18, 2015
A driving distance is 250 km. The distance shown on a map is 5cm. What is the scale factor?
Oct 15­8:11 PM
8.4 Scale Factors and Areas of 2‐D Shapes
Learning Goals:
1.
Demonstrate understanding of how the areas of similar shapes are related by their scale factor.
2.
Calculate a scale factor using measurements from similar shapes.
3.
Use scale factors to solve problems.
L
Oct 15­8:12 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
December 18, 2015
Key Ideas:
When a 2‐D shape undergoes an enlargement or reduction by a scale factor, k, the resulting shape is similar to the original shape.
If two 2‐D shapes are similar and their dimensions are related by a scale factor, k, then the relationship between the area of the similar shape and the area of the original shape can be expressed as:
Area of Similar 2D shape = k2 x (Area of Original Shape)
This formula can be rearranged to determine the scale factor if you know the areas of the two shapes.
Oct 15­8:13 PM
Ex(1)
A 3 cm x 5 cm rectangle has been enlarged by a scale factor of 2 to create a similar rectangle. How are their areas related?
Oct 15­8:14 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(2)
December 18, 2015
A triangle whose area is 76 cm2 will be reduced by a scale factor of 5/8. Determine the area of the reduced triangle to the nearest square centimetre.
Oct 15­8:16 PM
You Try:
A circle of area 10 cm2 will be enlarged by a scale factor of 5. Determine the area of the enlarged circle.
Oct 15­8:17 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(3)
December 18, 2015
The area of a parallelogram is 900 mm2. The area of a smaller, similar parallelogram is 100 mm2. What scale factor was used to make this reduction?
Oct 15­8:17 PM
You Try:
A trapezoid was reduced from an area of 750 mm2 to 30 mm2. What scale factor was used to make this reduction?
Oct 15­8:18 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(4)
December 18, 2015
Jasmine is making a kite from a 2:25 scale diagram. The area of the scale diagram is 20 cm2. How much fabric will she need for her kite?
Oct 15­8:18 PM
You Try:
Suppose Jasmine’s scale diagram for the kite had been drawn using a ratio of 1:20, and the area of the scale diagram had been 30 cm2. How much fabric would Jasmine have needed for her kite?
Oct 15­8:19 PM
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Day 2 ­ Scale Factor and Area of 2D(BLANK).notebook
Ex(5)
December 18, 2015
A computer screen measures 35 cm by 55 cm. An image on the computer is projected onto a whiteboard with a screen area of 7238 cm2. Determine the length and width of the whiteboard to the nearest cm.
Oct 15­8:19 PM
Questions to Try
p. 479‐482, # 1‐4, 6, 7, 11‐15
p. 487‐489, # 1‐3, 6, 7, 9, 10, 13, 14
Oct 15­8:20 PM
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