Geometry and Measurement
Core concepts
This domain covers two- and three-dimensional shapes and their properties, perimeter, area, volume, and surface area, angle relationships, triangle classification and the 180° angle sum, circles (C = πd, A = πr²), the coordinate plane, transformations (translation, rotation, reflection, dilation), and measurement conversion including elapsed time and money. Expect both direct formula application and multi-step problems involving composite figures.
Common traps
- Perimeter and area are not interchangeable; perimeter is a linear distance, area is measured in square units, volume in cubic units.
- Triangle and parallelogram area formulas need the perpendicular height, not a slanted side length.
- Doubling the radius of a circle quadruples its area, because the radius is squared.
- Convert units before computing. Remember that 1 m² = 10,000 cm², not 100 cm², since both dimensions convert.
- Complementary angles sum to 90°; supplementary angles sum to 180°. Vertical angles are equal.
- Dilation changes size but preserves shape and angle measures; the other three transformations preserve size as well.
Worked example
Find the area of a triangle with base 14 inches and height 9 inches. A = ½ × b × h = ½ × 14 × 9 = 63 square inches. If the problem instead gave a slanted side of 11 inches, that value is a distractor; only the perpendicular height belongs in the formula.
A conversion check: 2.4 km = 2,400 m, because multiplying by 1,000 moves the decimal three places right.
Rule of thumb: label every answer with its unit, and ask whether the unit should be linear, squared, or cubed before you finish.