Study guide
3.8 Geometry Basics
ATI TEAS 7 Nursing Admission
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1 Introduction to the ATI TEAS 7
1.1 About the ATI TEAS 7 Exam 1.2 Content Area Breakdown 1.3 Scoring and Program Requirements 1.4 Building Your TEAS Study Plan
2 Reading
2.1 Identifying the Main Idea 2.2 Making Inferences and Drawing Conclusions 2.3 Summarizing and Paraphrasing 2.4 Understanding Text Structure 2.5 Author's Purpose, Tone, and Point of View 2.6 Evaluating Arguments, Evidence, and Credibility 2.7 Integrating Information and Interpreting Graphics 2.8 TEAS Reading Strategies, Pacing, and Practice
3 Mathematics
3.1 Whole Numbers and Basic Operations 3.2 Fractions 3.3 Decimals and Percentages 3.4 Ratios and Proportions 3.5 Algebra and Equations 3.6 Measurement and Unit Conversions 3.7 Statistics and Data Interpretation 3.8 Geometry Basics
4 Science
4.1 The Cardiovascular System 4.2 The Respiratory System 4.3 The Digestive System 4.4 The Nervous System 4.5 The Musculoskeletal System 4.6 The Urinary and Reproductive Systems 4.7 Cell Biology and Genetics 4.8 Chemistry Basics 4.9 Scientific Reasoning and the Scientific Method
5 English & Language Usage
5.1 Grammar and the Parts of Speech 5.2 Sentence Structure 5.3 Punctuation 5.4 Spelling and Word Usage 5.5 Vocabulary in Context and Word Parts 5.6 Paragraph Organization and the Writing Process 5.7 Formal vs. Informal Language, Audience, and Tone 5.8 TEAS English Section Strategies and Pacing
3.8 Geometry Basics
Key Takeaways Explain This Topic AI
Area formulas to memorize: rectangle = l × w; triangle = ½ × b × h; circle = πr²; use π ≈ 3.14
Volume formulas: rectangular prism = l × w × h; cylinder = πr²h; report volume in cubic units
Perimeter is the distance around a shape; a circle's perimeter is its circumference, C = 2πr or πd
The Pythagorean theorem a² + b² = c² finds a missing side of a right triangle, where c is the hypotenuse
- Triangle angles sum to 180°; complementary angles sum to 90°; supplementary angles sum to 180°
- Last updated: October 2026
Why Geometry Is on the TEAS
Geometry questions live in the Measurement and Data area and ask you to find the perimeter, area, or volume of common shapes, to use basic angle facts, and to apply the Pythagorean theorem . In healthcare these skills size a wound or pressure injury (area), estimate fluid in a container (volume), and underpin imaging and body-surface-area dosing. The exam supplies the value π ≈ 3.14 ; the rest is selecting the correct formula and substituting carefully.
Common Shapes and Their Properties
- Shape Key Properties
- Triangle 3 sides; interior angles sum to 180°
- Rectangle 4 sides; opposite sides equal; 4 right angles
- Square 4 equal sides; 4 right angles (a special rectangle)
- Circle All points equidistant from the center; radius = half the diameter
- Parallelogram Opposite sides parallel and equal
- Trapezoid Exactly one pair of parallel sides
- Perimeter and Circumference
Perimeter is the total distance around a flat shape, measured in length units (cm, in). For a circle this distance is called the circumference .
- Shape Formula Example
- Rectangle P = 2l + 2w l=5, w=3 → P = 2(5)+2(3) = 16
- Square P = 4s s=4 → P = 16
- Triangle P = a + b + c 3, 4, 5 → P = 12
- Circle (circumference) C = 2πr or πd r=5 → C = 2π(5) ≈ 31.4
- Area
Area is the space inside a flat shape, measured in square units (cm², in²). Memorize this short list of area formulas.
- Shape Formula Example
- Rectangle A = l × w l=5, w=3 → A = 15
- Square A = s² s=4 → A = 16
- Triangle A = ½ × b × h b=6, h=4 → A = 12
- Circle A = πr² r=5 → A = 25π ≈ 78.5
- Parallelogram A = b × h b=8, h=5 → A = 40
- Trapezoid A = ½(b₁ + b₂) × h bases 4, 6; h=3 → A = 15
Worked Example (circle area): Find the area of a circle with radius 6 cm using π ≈ 3.14. A = πr² = 3.14 × 6² = 3.14 × 36 = 113.04 cm² . A common error is multiplying π by the radius before squaring — always square the radius first.
Volume
Volume is the space inside a 3-D solid, measured in cubic units (cm³, in³). Recall that 1 mL = 1 cm³ , linking volume to liquid dosing.
- Solid Formula Example
- Rectangular prism (box) V = l × w × h 8 × 5 × 3 → V = 120 cm³
- Cube V = s³ s=4 → V = 64 cm³
- Cylinder V = πr²h r=2, h=10 → V ≈ 125.6 cm³
Worked Example (box volume): A medicine box measures 8 cm × 5 cm × 3 cm. V = l × w × h = 8 × 5 × 3 = 120 cm³ . Because the result is a volume, the unit is cubic centimeters.
Angle Relationships
Angles are measured in degrees (°). The TEAS tests a few fixed sums you should memorize.
Right angle: exactly 90° (a square corner).
Straight angle: exactly 180° (a straight line).
Complementary angles: two angles that add to 90° .
Supplementary angles: two angles that add to 180° .
Triangle angle sum: the three interior angles of ANY triangle add to 180° .
Worked Example (missing angle): A right triangle has one angle of 35°. The right angle is 90°, so the third angle is 180° - 90° - 35° = 55° .
The Pythagorean Theorem
For any right triangle , the squares of the two legs add to the square of the hypotenuse (the side opposite the right angle, always the longest): a² + b² = c² , where c is the hypotenuse. Use it to find a missing side when the triangle has a right angle.
Worked Example: A right triangle has legs of 3 and 4. Find the hypotenuse. c² = a² + b² = 3² + 4² = 9 + 16 = 25 , so c = √25 = 5 . The 3-4-5 triangle is a classic set worth memorizing; another is 5-12-13.
Putting Units in the Right Place
A reliable way to avoid careless errors is to track units: length problems give plain units (cm), area problems give square units (cm²), and volume problems give cubic units (cm³). If your answer's units don't match what the question asks for, you used the wrong formula.
Recap
Match the shape to its formula: perimeter (and circumference) for distance around, area in square units for flat space, volume in cubic units for solid space, using π ≈ 3.14 and squaring the radius before multiplying. Lean on the fixed angle facts — 90° complementary, 180° supplementary, 180° triangle sum — and reach for a² + b² = c² whenever a right triangle hides a missing side.