Measurement and Geometry
The Measurement and Geometry domain tests your command of units and conversions, perimeter, area, volume and surface area, angle relationships in polygons, circle formulas, the coordinate plane, transformations, similarity and congruence, and the Pythagorean theorem - including choosing the right formula for a described situation.
Units and conversion
- Convert by multiplying by a ratio equal to 1, such as 100 cm/1 m: 3.5 m = 350 cm.
- Area units square the linear conversion factor (1 m² = 10,000 cm²); volume units cube it (1 m³ = 1,000,000 cm³).
Angles and polygons
- Triangle angles sum to 180°; quadrilateral angles sum to 360°. For an n-gon, the interior sum is (n − 2)·180°.
- Complementary angles sum to 90°; supplementary angles sum to 180°.
- Vertical angles are equal; angles on a straight line are supplementary.
Circles and solids
- Circumference C = πd = 2πr; area A = πr².
- Volume of a prism or cylinder is base area times height: V = Bh, and for a cylinder V = πr²h.
Worked example
A right triangle has legs 6 cm and 8 cm. The hypotenuse is √(6² + 8²) = √(36 + 64) = √100 = 10 cm. The area is ½(6)(8) = 24 cm², and the perimeter is 6 + 8 + 10 = 24 cm. Both numbers equal 24, but one is measured in square centimeters and the other in centimeters, so they are not comparable quantities - a favorite distractor.
Traps that cost marks
- Substituting the diameter where the formula calls for the radius.
- Forgetting that a scale factor k changes area by k² and volume by k³.
- Mixing perimeter, area, and surface area formulas for the same figure.
- Applying the Pythagorean theorem to a triangle without confirming the right angle.