Key Takeaways
- Perimeter is distance around; area is space inside
- Area is in square units; volume is in cubic units
- Circle formulas use π ≈ 3.14
- Memorize common measurement conversions
- Use visual models and manipulatives to teach geometry
Last updated: January 2026
Geometry and Measurement
The ParaPro tests basic geometry concepts including shapes, area, perimeter, and measurement conversions.
Basic Geometric Shapes
| Shape | Properties |
|---|---|
| Triangle | 3 sides, 3 angles (sum = 180°) |
| Rectangle | 4 sides, 4 right angles, opposite sides equal |
| Square | 4 equal sides, 4 right angles |
| Circle | All points equidistant from center |
| Parallelogram | 4 sides, opposite sides parallel and equal |
Perimeter
Perimeter is the distance around a shape.
Formulas:
- Rectangle: P = 2l + 2w (or 2(l + w))
- Square: P = 4s
- Triangle: P = a + b + c (sum of all sides)
Example: Rectangle with length 8 and width 5
- P = 2(8) + 2(5) = 16 + 10 = 26 units
Area
Area is the space inside a shape, measured in square units.
Formulas:
- Rectangle: A = l × w
- Square: A = s²
- Triangle: A = ½ × b × h
- Circle: A = πr²
Example: Rectangle with length 8 and width 5
- A = 8 × 5 = 40 square units
Circles
| Term | Definition | Formula |
|---|---|---|
| Radius (r) | Center to edge | — |
| Diameter (d) | Edge to edge through center | d = 2r |
| Circumference | Distance around | C = 2πr or πd |
| Area | Space inside | A = πr² |
Note: π ≈ 3.14 (often given on test)
Volume
Volume is the space inside a 3D shape, measured in cubic units.
Formulas:
- Rectangular prism: V = l × w × h
- Cube: V = s³
- Cylinder: V = πr²h
Measurement Conversions
Length (US Customary):
| Unit | Equivalence |
|---|---|
| 1 foot | 12 inches |
| 1 yard | 3 feet |
| 1 mile | 5,280 feet |
Length (Metric):
| Unit | Equivalence |
|---|---|
| 1 centimeter | 10 millimeters |
| 1 meter | 100 centimeters |
| 1 kilometer | 1,000 meters |
Weight/Mass:
| US Customary | Metric |
|---|---|
| 16 oz = 1 lb | 1,000 g = 1 kg |
| 2,000 lbs = 1 ton | 1,000 mg = 1 g |
Capacity:
| US Customary | Metric |
|---|---|
| 8 fl oz = 1 cup | 1,000 mL = 1 L |
| 2 cups = 1 pint | 1,000 L = 1 kL |
| 4 quarts = 1 gallon |
Classroom Application
Help students with geometry and measurement by:
- Using manipulatives (pattern blocks, rulers, measuring cups)
- Drawing shapes and labeling parts
- Creating conversion charts for reference
- Using real-world contexts (room dimensions, cooking)
- Teaching formulas with visual derivations
Test Your Knowledge
What is the area of a rectangle with length 12 cm and width 5 cm?
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B
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D
Test Your Knowledge
How many inches are in 3 feet?
A
B
C
D