Key Takeaways
- Triangle angles sum to 180°; quadrilateral angles sum to 360°
- Area of triangle = ½ × base × height
- Volume of rectangular prism = length × width × height
- Mean = average; Median = middle; Mode = most frequent
- Standard conversions: 12 in = 1 ft, 2 cups = 1 pint, 4 quarts = 1 gallon
Last updated: January 2026
2.3 Geometry, Measurement, and Data
This section covers geometric shapes, measurement concepts, and data analysis (about 30% of the Mathematics subtest).
Basic Geometric Shapes
2D Shapes:
| Shape | Properties |
|---|---|
| Triangle | 3 sides, 3 angles, angles sum to 180° |
| Quadrilateral | 4 sides, 4 angles, angles sum to 360° |
| Pentagon | 5 sides |
| Hexagon | 6 sides |
| Circle | No sides, defined by radius/diameter |
Types of triangles:
- By sides: Equilateral (3 equal), Isosceles (2 equal), Scalene (0 equal)
- By angles: Acute (all < 90°), Right (one 90°), Obtuse (one > 90°)
Types of quadrilaterals:
- Rectangle: 4 right angles
- Square: 4 right angles, 4 equal sides
- Parallelogram: 2 pairs of parallel sides
- Rhombus: 4 equal sides
- Trapezoid: Exactly 1 pair of parallel sides
Perimeter and Area
Perimeter: Distance around a shape
| Shape | Perimeter Formula |
|---|---|
| Rectangle | P = 2l + 2w |
| Square | P = 4s |
| Triangle | P = a + b + c |
| Circle (Circumference) | C = 2πr or πd |
Area: Space inside a shape
| Shape | Area Formula |
|---|---|
| Rectangle | A = l × w |
| Square | A = s² |
| Triangle | A = ½ × b × h |
| Parallelogram | A = b × h |
| Circle | A = πr² |
Volume
Volume: Space inside a 3D shape
| Shape | Volume Formula |
|---|---|
| Rectangular prism | V = l × w × h |
| Cube | V = s³ |
Measurement Conversions
Length:
- 12 inches = 1 foot
- 3 feet = 1 yard
- 5,280 feet = 1 mile
Capacity:
- 8 fluid ounces = 1 cup
- 2 cups = 1 pint
- 2 pints = 1 quart
- 4 quarts = 1 gallon
Weight:
- 16 ounces = 1 pound
- 2,000 pounds = 1 ton
Data and Statistics
Measures of central tendency:
- Mean (average): Sum of values ÷ number of values
- Median: Middle value when arranged in order
- Mode: Most frequent value
- Range: Highest - Lowest
Example: Data set: 3, 5, 5, 7, 10
- Mean: (3+5+5+7+10) ÷ 5 = 30 ÷ 5 = 6
- Median: 5 (middle value)
- Mode: 5 (appears most often)
- Range: 10 - 3 = 7
Test Your Knowledge
What is the area of a triangle with a base of 8 cm and a height of 5 cm?
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B
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D
Test Your Knowledge
Which type of quadrilateral has exactly one pair of parallel sides?
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B
C
D
Test Your Knowledge
Find the median of this data set: 12, 5, 8, 15, 3
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B
C
D
Test Your Knowledge
How many cups are in 2 quarts?
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B
C
D