Key Takeaways
- Area formulas: rectangle = l×w; triangle = ½×b×h; circle = πr²
- Volume formulas: rectangular prism = l×w×h; cylinder = πr²h
- Pythagorean theorem for right triangles: a² + b² = c²
- Triangle angles sum to 180°; complementary angles sum to 90°; supplementary sum to 180°
- Use π ≈ 3.14 for circle calculations on the TEAS
Geometry Basics
The TEAS tests basic geometry concepts including perimeter, area, volume, and properties of shapes. These skills apply to healthcare in dosing, wound measurement, and understanding medical imaging.
Basic Shapes and Properties
| Shape | Properties |
|---|---|
| Triangle | 3 sides, angles sum to 180° |
| Rectangle | 4 sides, opposite sides equal, 4 right angles |
| Square | 4 equal sides, 4 right angles |
| Circle | All points equidistant from center |
| Parallelogram | Opposite sides parallel and equal |
| Trapezoid | One pair of parallel sides |
Perimeter
Perimeter is the distance around a shape.
| Shape | Formula | Example |
|---|---|---|
| Rectangle | P = 2l + 2w | l=5, w=3: P = 2(5) + 2(3) = 16 |
| Square | P = 4s | s=4: P = 4(4) = 16 |
| Triangle | P = a + b + c | sides 3,4,5: P = 12 |
| Circle (Circumference) | C = 2πr or πd | r=5: C = 2π(5) = 10π ≈ 31.4 |
Area
Area is the space inside a shape, measured in square units.
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = l × w | l=5, w=3: A = 15 sq units |
| Square | A = s² | s=4: A = 16 sq units |
| Triangle | A = ½ × b × h | b=6, h=4: A = 12 sq units |
| Circle | A = πr² | r=5: A = 25π ≈ 78.5 sq units |
| Parallelogram | A = b × h | b=8, h=5: A = 40 sq units |
| Trapezoid | A = ½(b₁ + b₂) × h | bases 4,6, h=3: A = 15 sq units |
Volume
Volume is the space inside a 3D shape, measured in cubic units.
| Shape | Formula | Example |
|---|---|---|
| Rectangular prism | V = l × w × h | 4×3×2: V = 24 cubic units |
| Cube | V = s³ | s=3: V = 27 cubic units |
| Cylinder | V = πr²h | r=2, h=5: V = 20π ≈ 62.8 cubic units |
| Sphere | V = (4/3)πr³ | r=3: V = 36π ≈ 113.1 cubic units |
| Cone | V = (1/3)πr²h | r=3, h=4: V = 12π ≈ 37.7 cubic units |
Angles
| Angle Type | Degrees | Description |
|---|---|---|
| Acute | < 90° | Sharp angle |
| Right | = 90° | Square corner |
| Obtuse | > 90° and < 180° | Wide angle |
| Straight | = 180° | Straight line |
Angle Relationships:
- Complementary: Sum = 90°
- Supplementary: Sum = 180°
- Vertical angles: Equal (formed by intersecting lines)
Pythagorean Theorem
For right triangles: a² + b² = c²
Where c is the hypotenuse (longest side, opposite the right angle).
Example: Find the hypotenuse if legs are 3 and 4.
- 3² + 4² = c²
- 9 + 16 = c²
- 25 = c²
- c = 5
Common Pythagorean Triples
| Triple | Example |
|---|---|
| 3-4-5 | Most common |
| 5-12-13 | |
| 8-15-17 | |
| 7-24-25 |
Coordinate Geometry
Coordinate plane: x-axis (horizontal), y-axis (vertical) Ordered pair: (x, y)
Distance Formula: d = √[(x₂-x₁)² + (y₂-y₁)²]
Midpoint Formula: M = ((x₁+x₂)/2, (y₁+y₂)/2)
Healthcare Geometry Applications
| Application | Geometry Concept |
|---|---|
| Wound measurement | Area of irregular shapes |
| Medication volume | Volume of cylinder (syringe) |
| Body surface area | Surface area formulas |
| Imaging interpretation | Shapes, angles, proportions |
| Bandage sizing | Circumference, perimeter |
Calculate the area of a circle with radius 6 cm. (Use π ≈ 3.14)
A rectangular medicine box measures 8 cm × 5 cm × 3 cm. What is its volume?
If one angle of a right triangle is 35°, what is the third angle?