Unit 1 Scale Drawings

Use 1:20 What is 8cm?

1.6m

Use 1:100 What is 19cm?

19m

Corresponding sides

Are in the same position in similar figures.

Similar Figures

Have the same shape but are not necessarily the same size.

Symmetrical

Identical on either side of a central line.

128 sq. inches

Nolan is building a bird house. The drawing has a scale of 1.5 inches : 4 inches. What is the area of the actual base of the bird house, if the dimensions in the drawing are 6 inches by 3 inches?

37.5 miles

Parker is on a road trip. The map he is using has a scale that reads 2 inches : 25 miles. The next rest stop is 3 inches away on the map. How far will Parker have to drive to the next rest stop?

26 cm

The Eiffel Tower is 312 meters tall. How tall would the building be on a scale model if the scale is 1 cm = 12 m

25 inches

The Empire State Building is 1250 feet tall. How tall would the building be on a scale model if the scale is 1 inch = 50 feet?

corresponding sides

The sides with the same relative position in two congruent figures .

1/8

A car has a length of 12 feet. The model of the car has a length of 1.5 feet. Determine the scale factor.

9 ft

A car has a scale of 1 inch to 3 feet. If the picture measures 3 inches across, then how many feet long is the actual car?

Scale Drawing

A drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount called the scale factor

24 units by 15 units

A game room has a floor that is 120 feet by 75 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. What are the dimensions of the scale drawing?

.5 or (1/2)

A garden snail moves one-sixth foot in one-third hour. Find the unit rate.

scale model

A model of a figure or object in which each of the measurements are proportional to the original.

208

A model rocket is built to the scale of 1 in = 30 ft. The actual rocket is 6240 feet tall. How tall is the model rocket in inches?

scale drawing

A proportional two-dimensional sketch of an object that accurately depicts the objects.

Unit rate

A ratio in which the second quantity in the comparison is one.

scale(of a model)

A ratio representing the constant of proportionality between a scale model.

46 feet

A drawing of a rectangular bedroom has dimensions of 6cm x 5.5cm. If 1 cm represents 2 feet, what is the actual perimeter of the bedroom?

208

A model rocket is built to the scale 1:30, or 1 inch = 30 feet. The actual rocket is 6240 feet tall. How tall is the model rocket in inches?

Reduction

A scale factor that results in a smaller copy. (Example: drawing a map of the school.)

0.5 miles

Kylie is going to walk from her house to her friend's house. A map shows that the two houses are 1/4 inch apart. If the scale on the map is 1 in : 2 mi. how far apart are the two houses?

scale factor

The ratio of two corresponding length in two similar figures.

Using the scale 1:10 What are the dimensions if the actual size is 3m by 4m

30cm by 40cm

Use 1:20 What is 90cm?

4.5cm

Using the scale 1:10 What are the dimensions if the actual size is 5m by 6m

50cm by 60cm

19.5 by 36

A bookcase measures 13 feet wide and 24 feet tall. What would the bookcase's measurements be on a scale drawing using the scale 3 cm:2 ft?

19.5 cm wide X 36 cm tall

A bookcase measures 13 feet wide and 24 feet tall. What would the bookcase's measurements be on a scale drawing using the scale 3 cm:2 ft?

135 square feet

A floor plan of Mia's new house has a scale of 1 inch : 12 feet. On he floor plan, Mia's bedroom is 1.25 inches by 0.75 inches. what is the actual area of Mia's bedroom?

30

A scale drawing of a car has a scale of 1 inch to 1/2 a foot. The actual length of the care is 15 feet. What is the length of the drawing?

788.48 sq. feet

A scale drawing of a dance floor has a length of 14cm and a width of 22cm. The scale is 5cm : 8ft. What is the actual area of the dance floor?

Enlargement

A scale factor that results in a larger copy. (Example: taking a picture to the store to have it printed in a larger size.)

1 in. = 6 ft

A scale model of an airplane has a wingspan of 7 inches (in.). In real life, the same airplane has a wingspan of 42 feet (ft). What is the scale of the model to real life?

3

A window in Josh's room has a height of 6 feet. Draw an illustration that shows the window drawn to a scale of 1 centimeter=2 feet.

36

Ariel made a scale drawing of a picnic area near the river. The scale of the drawing was 1 inch = 3 yards. If the picnic area is 12 inches in the drawing, how wide is the actual picnic area?

26 2/3 feet

At Mount Rushmore, the sculpture of Teddy Roosevelt's head is approximately 80 feet in height. If his head was approximately 3/4 foot in height and his mouth was 3 inches long, how long is the mouth on the sculpture at Mount Rushmore?

A: 81 sq. units P: 36 units

Find the perimeter and area of a square (side length 4.5) when it is enlarged by a scale factor of 2.

29 inches

If 1 inch = 55 miles on a map, then how many inches will represent 1595 miles on the map?

2.8 or (2 and 8/10)

Julio walks 3.5 miles in 1.25 hours. Find the unit rate

80cm by 60cm

Marie has a small copy of Rene Magritte's famous painting, The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The scale of the copy is 1 in.:40 cm. Find the dimensions of the original painting.

129 miles

Ms. Jackson is driving from South Bend to Indianapolis. She measures a distance of 4.3 cm between the cities on her map. What is the actual distance between the cities if the map scale is 1 cm = 30 miles?

Asymmetry

Not identical on either side of a central line.

9 feet

On a blueprint, the scale is 1/2 inch = 10 feet. What is the actual height of the living room which is 9/20 inch on the blueprint?

75 miles

On a road map, the distance between 2 citites is 2.5 inches. The map scale is 1 inch = 30 miles. What is the actual distance between the cities?

135 inches

On a scale drawing, a tree is 6 3/4 inches tall. The scale factor is 1/20. Find the height of the actual tree.

84 inches

On a scale drawing, the scale factor is 1/12. A plum tree is 7 inches tall on the scale drawing. What is the actual height of the tree?

80

The model of an airplane has a wingspan of 20 inches. The model has a scale of 1 inch = 4 feet. What is the wingspan of the actual airplane?

3

The original image has a height of 2cm, the drawing has a height of 6cm. Determine the scale factor.

1/4

The scale drawing of a building has a height of 5 inches. The actual building is 20 feet high. How many inches in the scale drawing represent one foot on the actual building?

1/48

The scale drawing of a building has a height of 5 inches. The actual building is 20 feet high. What is the scale factor?

1

Using the scale, how long will Chelsey's 8-foot mirror be in the scale drawing? Scale: 1/2 inch = 4 feet

1 inch

Using the scale, how long will Chelsey's 8-foot mirror be in the scale drawing? Scale: 1/2 inch = 4 feet

The scale drawing has 1/4 the area of the original.

You have a 4 x 6 rectangle that you will reduce by a scale factor of 1/2. Compare what happens to the areas.

Use 1:50 Find the actual measurements if the model shows 7cm by 9cm

3.5m by 4.5m

The area of the scale drawing is 16 times the the area of the original.

A triangle has a height of 2 units and a base of 4 units. You will increase the triangle by a scale factor of 4. Compare what happens to the areas.

15

Bob makes a scale drawing of a statue using the scale 1 cm:5 ft. His drawing measures 12 cm. Kia makes a scale drawing of the same statue using the scale 1 cm:4 ft. How many centimeters tall is the statue in Kia's drawing?

15

Bridget measured the auditorium and made a scale drawing. The scale she used was 1 inch = 4 feet. The actual length of the stage is 60 feet. How long is the stage in the drawing?

(base=18m, slanted side=12m)

Draw a figure that is a dilation of the Parallelogram shown with a scale factor of 3/2.

(Square with side length of 2 inches)

Draw a figure that is a dilation of the given square with a scale factor of 1/3.

156.5 cm

For a school project, LeeAnn is making a model of the Empire State Building. She is using a scale of 1 cm = 8 feet. The Empire State Building is 1,252 feet tall. How tall is her model?

8

Haley made a scale drawing of a house and its lot. The scale she used was 1 inch = 6 feet. If the actual width of the backyard deck is 48 feet, how wide is the deck in the drawing?

28

Ruben made a scale drawing of the elementary school. The scale he used was 1 centimeter = 7 meters. The school yard is 4 centimeters in the drawing. How wide is the actual school yard?

corresponding angles

Two nonadjacent angles formed by crossing or two lines by a transversal one angle in the interior of two lines the other angle in the exterior of the two lines and both positioned on the same side of the transversal angles in the same relative position in two or more polygons that have an equal number of sides.

Rate

when you compare ratios of two different units like miles and hours

Ratio

when you compare two amounts of something; written three ways (3 to 2, 3/2, 3:2)

proportion

when you have two ratios that are equal even though they may have different numbers

Use 1:50 Find the actual measurements if the model shows 6cm by 7cm

3m by 3.5m

Use 1:100 What is 7m?

7cm

Scale Factor

A ratio that compares the sizes of the parts of one figure or object to the sizes of the corresponding parts of a similar figure or object. In this course it is also referred to as the multiplier.

1 inch high and 7 inches wide

A rectangular wall is 4 feet high and 28 feet wide. Which dimensions could be used to draw a similar model?

24.75 feet

A scale drawing of a billboard uses the scale 4 cm : 9 ft. The length of the billboard in the drawing is 11 cm. How long is the actual billboard?

24.75

A scale drawing of a billboard uses the scale 4 cm:9 ft. The length of the billboard in the drawing is 11 cm. How long is the actual billboard?

(window height should be 3 cm)

A window in Josh's room has a height of 6 feet. Draw an illustration that shows the window drawn to a scale of 1 centimeter=2 feet.

15cm

Bob makes a scale drawing of a statue using the scale 1 cm:5 ft. His drawing measures 12 cm. Kia makes a scale drawing of the same statue using the scale 1 cm:4 ft. How many centimeters tall is the statue in Kia's drawing?

4,800 sq. cm.

Marie has a small copy of Rene Magritte's famous painting, The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The scale of the copy is 1 in.:40 cm. Find the area of the ORIGINAL painting.

16

Mark measured a swimming pool and made a scale drawing. The scale of the drawing was 1 centimeter = 4 meters. In the drawing, the pool is 4 centimeters wide. What is the width of the actual pool?

3

Figure Y is a dilation of Figure X. Which scale factor was used to create Figure Y?

16 cm

For a school project, LeeAnn is making a model of the Empire State Building. She is using a scale of 1 cm = 8 feet. The Empire State Building is 128 feet tall. How tall is her model?

4.25 inches

If a building's actual length is 34 feet, what would it's size be on a scale drawing? The scale is 1 inch = 8 feet

You multiply each side of the shape by 3.5.

If you want to increase a shape by a scale factor of 3.5 what would you do to each side of the shape?

625 sq. feet

Joanne has a scale drawing of her backyard that includes a garden bed that measures 16 inches long and 25 inches wide. What is the area of the actual garden bed? Scale: 4in : 5ft

96

Jorge's printer can print 24 pages in 15 minutes. How many pages can it print in 1 hour?

3.5 inches

Josh wants to add a model of a tree to his model railroad layout. How big should the model tree be if the actual tree is 315 inches and the scale is 1:90?

4

Keenan drew a scale drawing of an arcade. The scale he used was 1 inch = 2 feet. If an air hockey table is 2 inches in the drawing, how wide is the actual air hockey table?

45 cm

Lacey is making a scale drawing of a field that is 150 yards long and 100 yards wide. If the field in Lacey's drawing is 30 centimeters wide, how long should the field be in the drawing?

21

Louie made a scale drawing of his room on grid paper, as shown. If each square on the grid paper represents a side length of 3 feet, what is the length, in feet, of the longest wall in his room?

4 2/5 inches

On a map of Georgia, the legend reads 1 inch = 25 miles. If the distance between Atlanta and Savannah is approximately 110 miles, what is the distance on the map, in inches, between the two cities?

27

On a map with a scale of 1 inch = 9 miles, the distance between two towns is 3 inches. What is the actual distance between the two towns?

18 in

On a map, 2 inches is 35 miles. The distance between Troy City and Ben City is 315 miles. How far apart are they on the map?

190 miles

On a road map of Virginia, the distance from Alexandria to Roanoke is 7.6 cm. What is the actual distance between the cities if the map scale is 2 cm = 50 miles?

54

On an architect's blueprint, the front of a building measures 27 inches. The scale of the blueprint is 1 inch = 2 feet. How wide will the front of the actual building be?

2

Sharon measured a summer camp and made a scale drawing. The scale she used was 1 centimeter = 9 meters. The actual length of the sand volleyball court is 18 meters. How long is the volleyball court in the drawing?

1/84

The actual measurement of the length of a pickup is 14 feet. If a model of the pickup measures 2 in. What is the scale factor?

23

The map of a park shows that a pond is 4 inches away from a playground. The scale of the map is 1 inch represents 5.75 meters. How far apart are the actual pond and playground?

2

The object in Figure JKLM is a dilation of the object in figure EFGH. Which scale factor was used to create the object in Figure JKLM?

60 inches

The scale factor for Maria's dollhouse furniture is 1:8. If the sofa in Maria's dollhouse is 7 1/2 inches long, how long is the actual sofa?

165 ft

The scale of a baseball bat to its enlarged replica is 2 inches to 10 feet. If a regular baseball bat is 33 inches, how tall would the replica be?

14

The scale on a road map indicates that 2 inches = 20 miles. How many inches would represent 140 miles on this road map?

1,100 miles

The scale on a road map is 1 cm = 500 miles. If the distance on the map between New York City and Memphis is 2.2 cm, what is the actual distance between the two cities?

1.8 miles

The scale on a wall map is 1 inch = 55 miles. What is the distance on the map between 2 cities that are 99 miles apart?

1.04 feet

There are several different scales in model railroading. Trains designated as O gauge are built to a scale factor of 1:48. To the nearest hundredth of a foot, how long is a model of a 50 foot boxcar in O gauge?

The scaled perimeter is 1/2 of the size.

You have a 4 x 6 rectangle that you will reduce by a scale factor of 1/2. Compare what happens to the perimeters.