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Grade 12 Challenge: Geometry Puzzles Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 6: 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 12 · 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 25 and one side of 7. What is its area?

Answer: 168

  1. 1

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

    Show your work
    Answer
  2. 2

    How many diagonals does a polygon with 14 sides have?

    Answer
  3. 3

    Each interior angle of a regular polygon is 162°. How many diagonals does it have?

    Show your work
    Answer
  4. 4

    5 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 circle fits exactly inside a square of side 11 (touching all four sides). What is the area of the circle in terms of π?

    Show your work
    Answer
  6. 6

    Each interior angle of a regular polygon is 144°. How many diagonals does it have?

    Show your work
    Answer
  7. 7

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

    Show your work
    Answer
  8. 8

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

    Show your work
    Answer
  9. 9

    A square is drawn inside a circle of radius 5 so its corners touch the circle. What is the area of the square?

    Show your work
    Answer
  10. 10

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

    Show your work
    Answer
  11. 11

    A square is drawn inside a circle of radius 2 so its corners touch the circle. What is the area of the square?

    Show your work
    Answer
  12. 12

    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

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/challenge_geometry

Answer key (click to show)
  1. 1.84
  2. 2.77
  3. 3.170
  4. 4.10
  5. 5.121π/4
  6. 6.35
  7. 7.35
  8. 8.20
  9. 9.50
  10. 10.120
  11. 11.8
  12. 12.16π

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Related worksheets

Challenge: Geometry Puzzles at other grades

Grade 10

More Grade 12 Math worksheets

Grade 12 Challenge: Algebra PuzzlesGrade 12 Challenge: Counting & ArrangementsGrade 12 Radians & the Unit CircleGrade 12 Trigonometric RatiosGrade 12 Trig Identities & EquationsGrade 12 Law of Sines & Law of CosinesGrade 12 VectorsGrade 12 Matrix Operations

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