Quiz: How well do you know the Perimeters and Areas of Similar Figures?

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| By Kriti Bisht
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Kriti Bisht
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Quizzes Created: 469 | Total Attempts: 82,166
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Quiz: How Well Do You Know The Perimeters And Areas Of Similar Figures? - Quiz

Dive into the captivating world of geometry with our quiz titled "How Well Do You Know the Perimeters and Areas of Similar Figures?" This engaging quiz is your opportunity to explore and test your expertise in calculating perimeters and areas within the realm of similar shapes. Spanning 15 thought-provoking questions, the quiz delves into various aspects of working with similar figures, offering you the chance to showcase your understanding. From uncovering the commonalities among similar figures to deciphering the intricate relationships between perimeters and areas, each question presents four options.

Whether you're a geometry aficionado seeking to challenge your understanding Read moreor a learner keen on honing your skills, this quiz is tailored to you. Prepare to embark on a journey of exploration, insights, and geometry mastery as you tackle the fascinating intricacies of perimeters and areas in similar figures. Dive in and discover the world of shapes and measurements like never before!


Questions and Answers
  • 1. 

    What do similar figures have in common?

    • A.

      Same shape

    • B.

      Same perimeter

    • C.

      Same area

    • D.

      Same angles

    Correct Answer
    A. Same shape
    Explanation
    Similar figures have the same shape but may differ in size. While angles remain congruent, lengths of corresponding sides are proportional, which leads to varying perimeters and areas.

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  • 2. 

    If one side of a triangle is proportionally doubled, how does the area change?

    • A.

      Doubled

    • B.

      Quadrupled

    • C.

      Halved

    • D.

      No change

    Correct Answer
    B. Quadrupled
    Explanation
    When a side of a triangle is doubled, its area becomes quadrupled due to the relationship between sides and areas in similar figures.

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  • 3. 

    What's the relationship between the perimeters of similar polygons?

    • A.

      Directly proportional

    • B.

      Inversely proportional

    • C.

      No relationship

    • D.

      Equal

    Correct Answer
    A. Directly proportional
    Explanation
    The perimeters of similar polygons are directly proportional to their corresponding sides. Doubling the side lengths results in a doubled perimeter, maintaining this linear relationship.

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  • 4. 

    How are the areas of similar triangles related if the ratio of their sides is k:1?

    • A.

      K^2 times

    • B.

      K times

    • C.

      K^3 times

    • D.

      K−1 times

    Correct Answer
    A. K^2 times
    Explanation
    The areas of similar triangles are proportional to the square of the ratio of their corresponding sides. This relationship is vital for solving problems involving similar triangles and their areas.

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  • 5. 

    If a rectangle's length and width are both doubled, how does the area change?

    • A.

      Doubled

    • B.

      Quadrupled

    • C.

      Halved

    • D.

      No change

    Correct Answer
    B. Quadrupled
    Explanation
    Doubling both the length and width of a rectangle results in its area becoming quadrupled, showcasing the relationship between area and side length changes in similar shapes.

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  • 6. 

    What's the ratio of the areas of two similar circles if their radii are in a 2:5 ratio?

    • A.

      2:5

    • B.

      4:25

    • C.

      5:2

    • D.

      25:4

    Correct Answer
    B. 4:25
    Explanation
    The ratio of the areas of two similar circles is the square of the ratio of their radii. In this case, the ratio of radii is 2:5, leading to an area ratio of 4:25.

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  • 7. 

    If the side length of a square is tripled, how does the area change?

    • A.

      Tripled

    • B.

      Nine times

    • C.

      Halved

    • D.

      No change

    Correct Answer
    B. Nine times
    Explanation
    When the side length of a square is tripled, its area increases by a factor of nine. This emphasizes the squared relationship between side length and area in square-shaped similar figures.

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  • 8. 

    What's true about the angles in similar figures?

    • A.

      They are congruent.

    • B.

      They are acute.

    • C.

      They are obtuse.

    • D.

      They vary.

    Correct Answer
    A. They are congruent.
    Explanation
    The angles in similar figures remain congruent. Regardless of size changes, corresponding angles maintain their measures, contributing to the overall similarity of the figures.

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  • 9. 

    How does the ratio of the areas of two similar rectangles change if their sides are doubled?

    • A.

      Doubled

    • B.

      Quadrupled

    • C.

      Halved

    • D.

      No change

    Correct Answer
    B. Quadrupled
    Explanation
    If the sides of two similar rectangles are doubled, their areas become quadrupled. This highlights the squared relationship between side lengths and areas in rectangles.

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  • 10. 

    If a triangle's height is halved while its base remains unchanged, how does the area change?

    • A.

      Halved

    • B.

      Doubled

    • C.

      Quadrupled

    • D.

      No change

    Correct Answer
    A. Halved
    Explanation
    When the height of a triangle is halved while the base remains unchanged, its area becomes halved. This demonstrates the proportional relationship between height and area in similar triangles.

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  • 11. 

    What's the relationship between the areas of similar polygons?

    • A.

      Directly proportional

    • B.

      Inversely proportional

    • C.

      No relationship

    • D.

      Equal

    Correct Answer
    A. Directly proportional
    Explanation
    The areas of similar polygons are directly proportional to the square of the ratio of their corresponding sides. This proportionality ensures that the areas grow or shrink consistently.

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  • 12. 

    How does the ratio of the perimeters of two similar squares change if their sides are doubled?

    • A.

      Doubled

    • B.

      Quadrupled

    • C.

      Halved

    • D.

      No change

    Correct Answer
    A. Doubled
    Explanation
    Doubling the sides of two similar squares results in a doubled perimeter ratio. This linear relationship between side lengths and perimeters remains consistent in square-shaped similar figures.

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  • 13. 

    What's the ratio of the perimeters of two similar rectangles if their sides are in a 3:4 ratio?

    • A.

      3:4

    • B.

      4:3

    • C.

      9:16

    • D.

      16:9

    Correct Answer
    A. 3:4
    Explanation
    The ratio of the perimeters of two similar rectangles is equal to the ratio of their corresponding sides. In this case, the ratio is 3:4, leading to a perimeter ratio of 3:4

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  • 14. 

    How does the area of a triangle change if its height and base are both doubled?

    • A.

      Doubled

    • B.

      Quadrupled

    • C.

      Halved

    • D.

      No change

    Correct Answer
    B. Quadrupled
    Explanation
    Doubling both the height and base of a triangle leads to a quadrupled area. This relationship highlights the direct relationship between the length of the base and the height of a triangle.

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  • 15. 

    What's the ratio of the areas of two similar squares if their side lengths are in a 1:3 ratio?

    • A.

      1:3

    • B.

      1:9

    • C.

      3:1

    • D.

      9:1

    Correct Answer
    B. 1:9
    Explanation
    The ratio of the areas of two similar squares is the square of the ratio of their side lengths. In this case, the ratio of side lengths is 1:3, resulting in an area ratio of 1:9.

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  • Current Version
  • Aug 10, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Aug 10, 2023
    Quiz Created by
    Kriti Bisht
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