← GED Geometry & Statistics Mastery

GED High School Equivalency Exam Study Guide

Key concepts, definitions, and exam tips organized by topic.

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GED Geometry & Statistics Mastery Study Guide


Overview

This study guide covers the essential geometry and statistics concepts tested on the GED Mathematical Reasoning exam. Topics include calculating perimeter, area, volume, surface area, applying the Pythagorean Theorem, analyzing angles, and interpreting statistical data. Mastering these concepts requires both memorizing key formulas and knowing when and how to apply them correctly.


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Section 1: Perimeter & Area


Summary

Perimeter measures the distance around a shape (linear units), while area measures the space inside a shape (square units). Each shape has its own formula — knowing which formula to use is just as important as calculating correctly.


Key Formulas


| Shape | Formula |

|---|---|

| Rectangle Perimeter | P = 2(l + w) |

| Triangle Area | A = ½ × b × h |

| Circle Area | A = π × r² |

| Circle Circumference | C = π × d or C = 2πr |

| Parallelogram Area | A = b × h |

| Trapezoid Area | A = ½ × (b₁ + b₂) × h |


Key Terms

  • • Perimeter – The total distance around the outside of a shape
  • • Area – The amount of surface space inside a shape, measured in square units
  • • Base (b) – The bottom side of a shape used in area calculations
  • • Height (h) – The perpendicular distance from the base to the opposite side or vertex
  • • Radius (r) – The distance from the center of a circle to its edge
  • • Diameter (d) – The distance across a circle through its center; d = 2r
  • • π (Pi) – Approximately 3.14; the ratio of a circle's circumference to its diameter

    • Important Relationships

  • • The diameter is always twice the radius: d = 2r, so r = d ÷ 2
  • • For a triangle, the height must be perpendicular (at a 90° angle) to the base — not just any side
  • • A parallelogram's area uses its vertical height, NOT the slanted side length
  • • A trapezoid has TWO parallel bases — both must be included in the formula

    • Watch Out For

    > ⚠️ Diameter vs. Radius Confusion — If a problem gives you the diameter, always divide by 2 to get the radius before using area or volume formulas. Forgetting this is one of the most common GED mistakes.


    > ⚠️ Units Matter — Area is always in square units (cm², ft², etc.) and perimeter is in linear units (cm, ft, etc.). Never mix them up on your answer.


    > ⚠️ Triangle Height — The height is not always a visible side of the triangle. It must be perpendicular to the base.


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    Section 2: Volume & Surface Area


    Summary

    Volume measures the amount of 3D space inside a solid figure (cubic units). Surface area measures the total area of all outer faces of a 3D figure (square units). The GED commonly tests rectangular prisms, cylinders, cones, spheres, and cubes.


    Key Formulas


    | Shape | Volume Formula |

    |---|---|

    | Rectangular Prism | V = l × w × h |

    | Cube | V = s³ |

    | Cylinder | V = π × r² × h |

    | Cone | V = ⅓ × π × r² × h |

    | Sphere | V = (4/3) × π × r³ |

    | Cube Surface Area | SA = 6 × s² |


    Key Terms

  • • Volume – The amount of 3D space enclosed by a solid figure, measured in cubic units
  • • Surface Area – The total area of all faces/surfaces of a 3D object, measured in square units
  • • Prism – A 3D figure with two identical parallel bases connected by rectangular faces
  • • Cylinder – A 3D figure with two circular bases and a curved surface
  • • Cone – A 3D figure with one circular base tapering to a point
  • • Sphere – A perfectly round 3D figure where every point on the surface is equidistant from the center

    • Important Relationships

  • • The cone's volume is exactly ⅓ of a cylinder with the same radius and height
  • • A cube is a special rectangular prism where all sides (s) are equal
  • • For cylinders, cones, and spheres — always confirm whether you have the radius or diameter before calculating

    • Watch Out For

    > ⚠️ Cubic Units — Volume answers must always be in cubic units (cm³, m³, in³). Writing square units for a volume answer will cost you points.


    > ⚠️ The ⅓ in Cone Volume — Students often forget to multiply by ⅓. Think of it as: a cone holds exactly one-third of what a cylinder holds.


    > ⚠️ Surface Area of a Cube — A cube has 6 faces, each with area s². So SA = 6s², not just s².


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    Section 3: Pythagorean Theorem & Angles


    Summary

    The Pythagorean Theorem applies exclusively to right triangles and relates the lengths of all three sides. Angle relationships — including complementary, supplementary, and triangle angle sums — are equally important for the GED.


    The Pythagorean Theorem

    a² + b² = c²

  • • a and b = the two legs (the shorter sides that form the right angle)
  • • c = the hypotenuse (the longest side, always opposite the right angle)

    • To find the hypotenuse: c = √(a² + b²)

    To find a missing leg: a = √(c² − b²)


    Common Pythagorean Triples (Memorize These!)

    | Leg (a) | Leg (b) | Hypotenuse (c) |

    |---|---|---|

    | 3 | 4 | 5 |

    | 5 | 12 | 13 |

    | 6 | 8 | 10 |

    | 8 | 15 | 17 |


    Key Angle Rules

  • • Triangle Angle Sum – All three angles in any triangle always add up to 180°
  • • Complementary Angles – Two angles that sum to 90°
  • • Supplementary Angles – Two angles that sum to 180°
  • • Right Angle – Exactly 90°, shown by a small square in diagrams

    • Key Terms

  • • Hypotenuse – The longest side of a right triangle, opposite the right angle
  • • Leg – Either of the two shorter sides of a right triangle that form the right angle
  • • Complementary – Two angles adding to 90°
  • • Supplementary – Two angles adding to 180°
  • • Right Triangle – A triangle containing exactly one 90° angle

    • Watch Out For

    > ⚠️ c is ALWAYS the hypotenuse — The variable c must represent the longest side. Never plug the hypotenuse in as a or b.


    > ⚠️ Pythagorean Theorem Only Works for Right Triangles — Do not attempt to use a² + b² = c² on triangles that don't have a 90° angle.


    > ⚠️ Complementary vs. Supplementary — Complementary = 90° (think "C" comes before "S," 90 comes before 180). Supplementary = 180°.


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    Section 4: Measures of Central Tendency


    Summary

    Measures of central tendency describe the center of a data set. The GED tests your ability to calculate and compare the mean, median, mode, and range — and to know which measure best represents a given data set.


    Definitions & How to Calculate


    | Measure | Definition | How to Calculate |

    |---|---|---|

    | Mean | The arithmetic average | Sum of all values ÷ number of values |

    | Median | The middle value | Arrange in order; find the center value |

    | Mode | The most frequent value | Find the value(s) that appear most often |

    | Range | The spread of the data | Maximum value − Minimum value |


    Step-by-Step: Finding the Median

    1. Arrange all values in order from least to greatest

    2. Count the number of values

    - Odd number of values → The median is the single middle value

    - Even number of values → The median is the average of the two middle values


    Example (even): Data set: 2, 5, 8, 11

    Two middle values = 5 and 8 → Median = (5 + 8) ÷ 2 = 6.5


    Key Terms

  • • Mean – The sum divided by the count; also called the "average"
  • • Median – The middle value when data is ordered; not affected by extreme values
  • • Mode – The most frequently occurring value; a data set can have no mode, one mode, or multiple modes
  • • Range – The difference between the highest and lowest values; measures spread, not center
  • • Outlier – An extreme value that can significantly affect the mean but not the median

    • Watch Out For

    > ⚠️ Always Sort Before Finding the Median — Finding the median of an unsorted list is the most common error. Always arrange values in order first.


    > ⚠️ Even-Numbered Data Sets — When there is an even number of values, there is no single middle number. You MUST average the two middle values.


    > ⚠️ Range ≠ Central Tendency — Range measures spread (variability), not the center of the data. Do not confuse it with mean or median.


    > ⚠️ No Mode is Possible — If every value appears only once, the data set has no mode. Do not write zero as the mode.


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    Section 5: Data Interpretation


    Summary

    The GED requires you to read and interpret data from bar graphs, pie charts, scatterplots, and stem-and-leaf plots. You must extract information accurately and perform calculations — often involving percentages — based on what the graph displays.


    Types of Graphs & Their Purposes


    | Graph Type | Best Used For |

    |---|---|

    | Bar Graph | Comparing quantities across categories |

    | Pie Chart | Showing parts of a whole (percentages) |

    | Scatterplot | Showing relationships/correlations between two variables |

    | Stem-and-Leaf Plot | Displaying distribution of numerical data while preserving actual values |

    | Line Graph | Showing change over time |


    Key Concepts


    #### Pie Charts & Percentages

  • • Part = Percentage × Whole
  • • Example: 25% of $2,400 = 0.25 × 2,400 = $600
  • • To find a percentage: (Part ÷ Whole) × 100

    • #### Scatterplot Correlations

  • • Positive Correlation – Points trend upward left to right (both variables increase together)
  • • Negative Correlation – Points trend downward left to right (as one increases, the other decreases)
  • • No Correlation – Points are scattered with no clear pattern

    • #### Stem-and-Leaf Plots

  • • The stem represents the leading digit(s) (e.g., tens place)
  • • The leaf represents the trailing digit (e.g., ones place)
  • • Example: Stem 4 | Leaf 2, 5 = values 42 and 45
  • • Always check if there is a key provided

    • Key Terms

  • • Bar Graph – A chart using rectangular bars to represent data values
  • • Pie Chart – A circular chart divided into sectors representing proportional parts of a whole
  • • Scatterplot – A graph of plotted points showing the relationship between two variables
  • • Stem-and-Leaf Plot – A display that splits data values into stems and leaves to show distribution
  • • Positive Correlation – A relationship where both variables increase together
  • • Negative Correlation – A relationship where one variable increases as the other decreases
  • • Correlation – The statistical relationship between two variables

    • Watch Out For

    > ⚠️ Read Graph Scales Carefully — Always check the axis labels and scale increments before reading values from a bar graph or line graph.


    > ⚠️ Percentage Calculations from Pie Charts — To find an amount from a percentage, convert the percent to a decimal first (25% → 0.25), then multiply by the total.


    > ⚠️ Correlation ≠ Causation — A scatterplot showing correlation does not prove that one variable causes the other to change. The GED may ask you to identify this distinction.


    > ⚠️ Stem-and-Leaf Requires a Key — Without reading the key, you may misinterpret what the stems and leaves represent.


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    Quick Review Checklist


    Use this checklist before your exam to confirm you are ready:


    Perimeter & Area

  • • [ ] I know the area formula for triangles, circles, parallelograms, and trapezoids
  • • [ ] I can calculate perimeter for rectangles and other polygons
  • • [ ] I can convert diameter to radius before using circle formulas
  • • [ ] I label my answers with the correct units (linear vs. square)

    • Volume & Surface Area

  • • [ ] I know volume formulas for prisms, cylinders, cones, and spheres
  • • [ ] I remember to multiply by ⅓ for cone volume
  • • [ ] I can calculate surface area of a cube (6s²)
  • • [ ] I label volume answers with cubic units

    • Pythagorean Theorem & Angles

  • • [ ] I can state the Pythagorean Theorem: a² + b² = c²
  • • [ ] I know c always represents the hypotenuse
  • • [ ] I can find a missing leg using √(c² − a²)
  • • [ ] I know the common triples: 3-4-5, 5-12-13, 6-8-10
  • • [ ] I know triangle angles sum to 180°, complementary = 90°, supplementary = 180°

    • Measures of Central Tendency

  • • [ ] I can calculate mean, median, mode, and range
  • • [ ] I always sort data before finding the median
  • • [ ] I can find the median of an even-numbered data set by averaging the two middle values
  • • [ ] I understand that range measures spread, not center

    • Data Interpretation

  • • [ ] I can read values accurately from bar graphs and pie charts
  • • [ ] I can calculate a dollar amount or count from a percentage using Part = % × Whole
  • • [ ] I can identify positive, negative, and no correlation on a scatterplot
  • • [ ] I can read a stem-and-leaf plot correctly using the key

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    Tip: On the GED, a formula sheet is provided — but you still need to know which formula to choose and how to apply it. Practice with timed problems to build both accuracy and speed.

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