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Grade 10 Challenge: Geometry Puzzles Worksheet with Answers

Grade 10 (US) · Year 11 (UK) · Class 10 (India) · Math

Unit 8: Going FurtherChallenge PuzzlesChallenge

Geometry puzzles about diagonals, inscribed shapes and hidden right triangles. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Geometry Puzzles

Grade 10 · Math

Score___ / 12

Name

Class

Date

Learning goal: Challenge Puzzles

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

A rectangle has a diagonal of 17 and one side of 8. What is its area?

Answer: 120

  1. 1

    How many diagonals does a polygon with 14 sides have?

    Answer
  2. 2

    A square is drawn inside a circle of radius 4 so its corners touch the circle. What is the area of the square?

    Show your work
    Answer
  3. 3

    8 points are marked on a circle. How many different triangles can be drawn using these points as corners?

    Show your work
    Answer
  4. 4

    12 points are marked on a circle. How many different triangles can be drawn using these points as corners?

    Show your work
    Answer
  5. 5

    A rectangle has a diagonal of 25 and one side of 7. What is its area?

    Answer
  6. 6

    Each interior angle of a regular polygon is 135°. How many diagonals does it have?

    Show your work
    Answer
  7. 7

    9 points are marked on a circle. How many different triangles can be drawn using these points as corners?

    Show your work
    Answer
  8. 8

    A circle fits exactly inside a square of side 10 (touching all four sides). What is the area of the circle in terms of π?

    Show your work
    Answer
  9. 9

    Each interior angle of a regular polygon is 156°. How many diagonals does it have?

    Show your work
    Answer
  10. 10

    A rectangle has a diagonal of 13 and one side of 5. What is its area?

    Answer
  11. 11

    A circle fits exactly inside a square of side 8 (touching all four sides). What is the area of the circle in terms of π?

    Show your work
    Answer
  12. 12

    A square is drawn inside a circle of radius 10 so its corners touch the circle. What is the area of the square?

    Show your work
    Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/10/challenge_geometry

Answer key (click to show)
  1. 1.77
  2. 2.32
  3. 3.56
  4. 4.220
  5. 5.168
  6. 6.20
  7. 7.84
  8. 8.25π
  9. 9.90
  10. 10.60
  11. 11.16π
  12. 12.200

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Related worksheets

Challenge: Geometry Puzzles at other grades

Grade 12

More Grade 10 Math worksheets

Grade 10 Challenge: Counting & ArrangementsGrade 10 Radians & the Unit CircleGrade 10 Law of Sines & Law of CosinesGrade 10 Coordinate GeometryGrade 10 Parallel & Perpendicular LinesGrade 10 Equations of CirclesGrade 10 Angles Formed by Parallel Lines & TransversalsGrade 10 Transformations on the Coordinate Plane

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