Students, teachers, and geometry enthusiasts - are you ready for a free, interactive challenge? Take our perimeters and areas of similar figures quiz to test your math skills! Whether you need perimeters and areas of similar figures practice or a quick geometry similarity quiz, you'll master scaling factors, proportional shapes, and essential calculations. Sharpen your perimeter and area practice with triangles, rectangles, and more while tracking accuracy and speed. Dive into our area skills challenge or tackle creative perimeter puzzles. Ready to ace every shape calculation? Let's go!
What is the perimeter of a square with side length 5 cm?
20 cm
15 cm
25 cm
10 cm
The perimeter of a square is 4 times its side length. Here, 4 × 5 cm = 20 cm. Each side contributes equally to the total. For more details, see Math is Fun: Square.
What is the area of a rectangle that measures 4 cm by 7 cm?
22 cm²
11 cm²
28 cm²
14 cm²
Area of a rectangle is length multiplied by width. So 4 cm × 7 cm = 28 cm². This formula applies to all rectangles. More info at Khan Academy: Area of Rectangle.
When a figure is enlarged by a scale factor of 2, how does its perimeter change?
It doubles
It quadruples
It remains the same
It triples
Perimeter scales linearly with the scale factor. If the linear scale factor is 2, the perimeter doubles. This holds true for all similar figures. See Math is Fun: Similar Figures.
If a figure is enlarged by a scale factor of 3, by what factor does its area change?
3
6
12
9
Area scales by the square of the linear scale factor. With factor 3, area increases by 3² = 9. This is a core property of similar figures. More at Khan Academy: Scale Factors and Area.
Two similar triangles have a scale factor of 2 (small to large). If the area of the smaller triangle is 9 cm², what is the area of the larger triangle?
12 cm²
24 cm²
18 cm²
36 cm²
The area scales by the square of the scale factor: 2² = 4. Multiply the smaller area by 4: 9 × 4 = 36 cm². This applies to all similar polygons. See Math is Fun: Similar Triangles.
A rectangle is similar to another rectangle. The shorter side of the first is 3 cm, and the corresponding side of the second is 9 cm. What is the area ratio (first:second)?
1:6
1:27
1:9
1:3
Linear scale factor = 3/9 = 1/3, but we want first to second so it's 3:9 = 1:3. Area ratio is (1/3)² = 1/9, or 1:9. See Khan Academy: Similar Figures.
A circle with radius 4 cm is enlarged to a circle with radius 10 cm. What is the ratio of their circumferences (small:large)?
1:2.5
4:5
4:10
2:5
Circumference is linear with radius. Ratio = 4:10 = 2:5 after simplifying. Because circumference = 2?r, the ? and 2 cancel in ratio. More at Math is Fun: Circle.
Two similar polygons have perimeters in ratio 5:7. If the smaller polygon's perimeter is 25 cm, what is the larger's perimeter?
28 cm
45 cm
30 cm
35 cm
Linear ratio = 5:7, so if small is 25 cm, one unit = 25/5 = 5 cm. Larger = 7 × 5 = 35 cm. The ratio directly applies to perimeters. Learn more at Khan Academy: Similar Figures Perimeter.
A triangle with area 6 cm² is similar to a larger triangle with linear scale factor 0.5 (large to small). What is the area of the smaller triangle?
3 cm²
1 cm²
1.5 cm²
2 cm²
Scale factor large:small = 0.5 means small:large = 2:1. Actually scale small relative = 0.5, so area scales by (0.5)² = 0.25. Multiply 6 cm² by 0.25 = 1.5 cm². See Math is Fun: Similarity.
Two similar rectangles have an area ratio of 16:25. What is the linear scale factor (first:second)?
8:10
16:25
2:3
4:5
Linear scale factor is the square root of area ratio: ?(16:25) = 4:5. This applies to all similar figures. For more, visit Khan Academy: Scale Factor.
A regular hexagon has side length 6 cm. Its similar scaled copy has side length 15 cm. What is the difference in perimeters between the two hexagons?
90 cm
36 cm
54 cm
24 cm
Original perimeter = 6 × 6 = 36 cm; scaled perimeter = 15 × 6 = 90 cm. Difference = 90 ? 36 = 54 cm. Perimeter scales linearly. See Math is Fun: Hexagon.
Two similar triangles have areas of 18 cm² and 50 cm². What is the ratio of their perimeters (small:large)?
6:10
3:5
18:50
9:25
Area ratio = 18:50 = 9:25. Linear ratio is ?(9:25) = 3:5, which equals the perimeter ratio. Learn more at Khan Academy: Similar Figures.
If two similar figures have perimeters in the ratio 4:9, what is the ratio of their areas?
4:9
2:3
16:81
8:18
Area ratio = (perimeter ratio)² = 4²:9² = 16:81. This holds for all similar shapes. More at Math is Fun: Similar Figures.
A rectangle has been scaled up by a factor of 2.5. If the original area was 40 cm², what is the new area?
A right triangle with legs 3 cm and 4 cm is scaled by factor 4. What is the area of the scaled triangle?
64 cm²
36 cm²
96 cm²
48 cm²
Original area = (3×4)/2 = 6 cm². Scale factor 4 gives area factor 4² = 16. New area = 6×16 = 96 cm². More at Math is Fun: Triangle Area.
Two similar rectangles have perimeters that differ by 18 cm. If the scale factor from the smaller to the larger is 1:2, what is the perimeter of the smaller rectangle?
24 cm
12 cm
9 cm
18 cm
Let small perimeter = P, large = 2P. Difference is 2P ? P = P = 18 cm, so P = 18 cm. This uses linear scaling directly with perimeters. More at Khan Academy: Scale Factor.
Two similar triangles have an area ratio of 49:81. If the difference in their heights is 4 cm, what is the difference in their corresponding base lengths?
10 cm
8 cm
4 cm
6 cm
Linear ratio = ?(49:81) = 7:9. Difference in corresponding measures = (9?7) units = 2 units. If height difference = 4 cm, then one unit = 2 cm. Base difference = 2 units × 2 cm = 4 cm? Actually the height difference measures 2 units = 4 cm means 1 unit = 2 cm, so base difference = (9?7)×2 = 4 cm. The correct difference is 4 cm, but 6 cm is incorrect here. See Math is Fun: Similar Triangles.
A square of unknown side length is scaled by a factor of k to produce another square. If the sum of their areas is 100 cm² and k = 2, what is the side length of the original square?
5 cm
?(100/5) cm
10 cm
?(100/3) cm
Let original side = s, scaled side = 2s. Areas sum: s² + (2s)² = s² + 4s² = 5s² = 100, so s² = 20 ? s = ?20 = ?(100/5). For more on area relations see Khan Academy: Similar Figures.
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AI Study Notes
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Study Outcomes
Understand similarity ratios -
Identify and compare scale factors between similar figures to see how side lengths correspond.
Calculate scaled perimeters -
Apply linear scale factors to original perimeters to find the perimeters of similar figures accurately.
Compute corresponding areas -
Use the square of the scale factor to determine the area of a similar figure based on its original.
Analyze shape transformations -
Examine how scaling impacts both perimeter and area across various geometric figures.
Apply problem-solving strategies -
Tackle perimeters and areas of similar figures practice questions with clear, step-by-step methods.
Evaluate your geometry skills -
Review quiz feedback to recognize strengths and identify areas for further perimeters and areas of similar figures quiz practice.
Cheat Sheet
Scale Factor and Perimeter Ratio -
When prepping for your perimeters and areas of similar figures quiz, remember that the ratio of perimeters matches the scale factor k of corresponding sides (P1/P2 = k). For instance, two similar triangles with side lengths 5 cm and 8 cm will have perimeters in a 5:8 ratio. This trick helps you quickly link side scaling to perimeter scaling.
Area Ratio as Square of Scale Factor -
In your geometry similarity quiz, note that the areas of similar figures scale by the square of the side ratio (A1/A2 = k²). For example, enlarging a pentagon by a factor of 4 makes the area 16 times greater. Use "scale factor squared for surface" as a quick memory phrase.
Solving for Unknown Side Lengths -
Often in a perimeters and areas of similar figures quiz, you'll solve equations like (side1/side2) = (P1/P2). Suppose two triangles have perimeters of 24 cm and 36 cm, then the side ratio is 2:3, so a 10 cm side corresponds to 15 cm. This approach blends algebraic skills with geometric insights.
Composite Figures and Scaling -
For perimeter and area practice with composite figures (like an L-shape), apply the overall scale factor to the total measurements - no need to recalculate each part separately. Use k for perimeters and k² for areas. Trusted resources like university geometry labs often offer practice problems on composite similar shapes for extra reinforcement.
Real-World Applications and Practice Techniques -
Blueprints, maps, and models all rely on similarity: a 1:100 scale on a map reduces lengths to 1% and areas to 0.01%. Practicing perimeters and areas of similar figures in context helps boost retention and confidence. Try labeling a floor plan with scaled measurements for fun geometry similarity quiz practice!
