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Quizzes > High School Quizzes > Mathematics

Scaled Copies Practice Quiz Worksheet

Practice your skills with our worksheet PDF

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting the Scaled Copies Challenge, a high school geometry trivia quiz.

If a square has a side length of 4 and is scaled by a factor of 3, what is the new side length?
12
9
7
8
Multiplying the original side length by the scaling factor yields the new side length. Here, 4 multiplied by 3 gives 12.
A rectangle measures 5 cm by 10 cm. If each dimension is scaled by a factor of 2, what is the new area in square centimeters?
250 cm²
150 cm²
100 cm²
200 cm²
Scaling both dimensions by 2 makes the new dimensions 10 cm and 20 cm. The area is then 10 à - 20 = 200 cm².
If a shape is scaled up by a factor of 4, how is its perimeter affected?
It becomes 4 times larger
It becomes 16 times larger
It is half as large
It is unchanged
Since the perimeter is a linear measurement, scaling by a factor of 4 means that each side is multiplied by 4, making the perimeter 4 times larger.
Two similar triangles have a scale factor of 2 from the smaller to the larger triangle. Which statement is true about their corresponding sides?
Each side in both triangles is the same length.
Each side in the larger triangle is four times as long.
Each side in the larger triangle is half as long as the corresponding side in the smaller triangle.
Each side in the larger triangle is twice as long as the corresponding side in the smaller triangle.
A scale factor of 2 directly indicates that every side length in the larger triangle is double that of the smaller triangle.
A circle has a radius of 3. When the circle is scaled by a factor of 5, what is the new circumference (using the formula 2Ï€r)?
30Ï€
10Ï€
25Ï€
15Ï€
Scaling the circle by a factor of 5 makes the new radius 3 Ã - 5 = 15. The new circumference is 2Ï€ Ã - 15, which equals 30Ï€.
A rectangle with dimensions 4 cm by 7 cm is scaled by a factor of 3. What is the ratio of the new perimeter to the original perimeter?
1:1
3:1
9:1
1:3
The perimeter scales linearly with every dimension. Therefore, a scaling factor of 3 means the new perimeter is 3 times the original.
Two similar figures have a scale factor of 1:3. If the area of the smaller figure is 8 cm², what is the area of the larger figure?
80 cm²
24 cm²
64 cm²
72 cm²
The area of similar figures scales as the square of the linear scale factor. Since 3² equals 9, the area of the larger figure is 8 à - 9 = 72 cm².
When a figure is reduced by a scale factor of 0.5, by what factor does the area change?
0.5
0.25
1
0.75
Since the area scales with the square of the scaling factor, reducing a figure by a factor of 0.5 reduces the area to 0.5² = 0.25 of the original.
A model car is built at a scale of 1:10 relative to the actual car. If the model car is 15 cm long, what is the length of the actual car?
15 cm
150 cm
75 cm
200 cm
A scale of 1:10 signifies that 1 unit on the model corresponds to 10 units in reality. Multiplying 15 cm by 10 results in an actual length of 150 cm.
Two similar polygons have corresponding side lengths in the ratio 2:5. What is the ratio of their areas?
4:25
5:2
25:4
2:5
The ratio of the areas of similar figures is the square of the ratio of their corresponding side lengths. In this case, (2/5)² results in 4:25.
If a triangle with a base of 6 cm and a height of 9 cm is scaled by a factor of 2, what is its new area?
54
81
216
108
The original area is 0.5 à - 6 à - 9 = 27 cm². Scaling by a factor of 2 multiplies the area by 2², resulting in 27 à - 4 = 108 cm².
A scale drawing of a park uses a scale where 1 cm represents 100 m. If a trail measures 3.5 cm on the drawing, what is its actual length?
300 m
3500 m
350 m
70 m
Multiplying the drawing measurement of 3.5 cm by the scale factor of 100 gives 3.5 Ã - 100 = 350 m for the actual length.
In similar figures, if the ratio of their perimeters is 3:4, what is the ratio of their corresponding side lengths?
4:3
9:16
3:4
16:9
Perimeters and corresponding side lengths scale linearly. Thus, if the perimeters are in the ratio 3:4, the side lengths share the same ratio.
A poster is enlarged from a 10 inch by 12 inch version to a 20 inch by 24 inch version. What is the scale factor and how does the area change?
Scale factor is 2; area increases by factor 4
Scale factor is 4; area increases by factor 16
Scale factor is 4; area increases by factor 4
Scale factor is 2; area increases by factor 2
Each linear dimension doubles, making the scale factor 2. The area, being a two-dimensional measure, increases by the square of the scale factor, which is 2² = 4.
A triangle with sides measuring 3, 4, and 5 is scaled by a factor of 3. What are the lengths of the sides of the new triangle?
6, 8, 10
9, 12, 15
3, 4, 5
9, 6, 15
Multiplying each original side by the scale factor of 3 yields the new side lengths: 3Ã - 3 = 9, 4Ã - 3 = 12, and 5Ã - 3 = 15.
An architect designs two similar buildings with a scale factor of 1:50 from the model to the actual structure. If a window in the model is 2 cm wide and has an area of 6 cm², what is the area of the actual window?
7500 cm²
15000 cm²
6000 cm²
300 cm²
Linear dimensions are scaled by 50, so the area scales by 50², which is 2500. Multiplying the model's window area of 6 cm² by 2500 results in an actual area of 15000 cm².
A pair of similar right triangles have hypotenuses in the ratio 3:7. If the smaller triangle has an area of 18 cm², what is the area of the larger triangle?
100 cm²
88 cm²
98 cm²
63 cm²
Since the triangles are similar, the ratio of their areas is the square of the ratio of their corresponding sides. The ratio (7/3)² equals 49/9, and multiplying 18 by 49/9 yields 98 cm².
A scaled drawing uses a scale factor of 0.25, meaning the drawing's dimensions are 0.25 times the actual dimensions. If a portion of the drawing measures 8 units in length and has an area of 64 square units, what are the actual length and area?
2 units and 4 square units
16 units and 256 square units
12 units and 144 square units
32 units and 1024 square units
The actual length is found by dividing 8 units by 0.25, which gives 32 units. Similarly, because area scales by the square of the linear scale factor (0.25² = 0.0625), dividing 64 by 0.0625 yields 1024 square units.
In a scale model of a park with a linear scale of 1:200, if a pond in the model has an area of 0.5 m², what is the actual area of the pond in square meters?
8000 m²
10000 m²
400 m²
20000 m²
The area in a scale model scales by the square of the linear scale factor. With a scale of 1:200, the area multiplies by 200² (which is 40000). Thus, 0.5 m² à - 40000 equals 20000 m².
When a three-dimensional solid is scaled by a factor of k, its volume changes by what factor? Specifically, if k = 3, by what factor does the volume change?
3
81
9
27
Volume is a three-dimensional measurement, so scaling the dimensions by a factor of k increases the volume by k³. For k = 3, the volume increases by 3³, which is 27.
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Study Outcomes

  1. Identify scale factors between similar figures.
  2. Calculate unknown dimensions in scaled geometric shapes.
  3. Apply proportional reasoning to solve scaling problems.
  4. Analyze the relationship between scaling and geometric properties such as area and perimeter.
  5. Evaluate the effects of scaling on measurements in real-world contexts.

Scaled Copies Worksheet PDF Cheat Sheet

  1. Scaled Copies Preserve Proportions - A scaled copy is like your favorite shape hitting the gym or chilling on vacation: it grows or shrinks but never loses its proportions. Every length is multiplied by the same scale factor, so angles and overall shape stay exactly the same - just at a different size. Lesson page Original source
  2. Scaling Side Lengths by a Factor - To create a scaled copy, you simply multiply each original side length by your chosen scale factor - no rocket science required! For example, a triangle with sides 3, 4, and 5 scaled by 2 turns into a 6‑8‑10 triangle, preserving that perfect right‑angle vibe. Lesson page Original source
  3. Triangle Proportionality Theorem - This theorem says if a line is drawn parallel to one side of a triangle, it splits the other two sides into matching proportional segments. It's like slicing a sandwich so that both halves have the same filling ratio - neat and balanced! Lesson page Original source
  4. Similar Triangles Have Proportional Sides - When triangles are similar, corresponding sides always share the same ratio. For instance, if one triangle is 3‑4‑5 and its twin's shortest side measures 6, the other sides must be 8 and 10 - no guesswork needed! Lesson page Original source
  5. Scale Drawings Use a Scale Factor - In scale drawings, 1 unit on paper corresponds to a fixed number of real‑world units. For example, a 1:100 scale means 1 cm on the drawing equals 100 cm in real life - perfect for architects and model‑makers! Lesson page Original source
  6. Proportional Reasoning with Real Examples - Proportional reasoning is all about setting up and solving ratios. If 1,000 lines of code run in 15 seconds, you can predict that 600 lines execute in 9 seconds by keeping those ratios tight and tidy. Lesson page Original source
  7. Proportional Line Segment Theorem - When three or more parallel lines cut across two transversals, they carve those transversals into proportional pieces. Think of ladder rungs slicing two beams - each gap lines up perfectly in ratio! Lesson page Original source
  8. Keep Corresponding Angles Equal - Similarity isn't just about side lengths - their angles must match too. Whenever you draw a scaled copy, double‑check that every angle looks identical to preserve that similarity seal of approval. Lesson page Original source
  9. Cross‑Multiplication for Complex Proportions - To crack tricky proportions, cross‑multiply and solve for your variable. For example, solving 20(x+4)=90 becomes a breeze once you distribute, subtract, and divide to find x=1. Lesson page Original source
  10. Practice Makes Perfect with Rectangles - Grab a rectangle with sides 2 and 3, scale it by 1.5, and you'll get 3 and 4.5 - simple drills like this build confidence faster than you can say "proportion!". Lesson page Original source
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