Geometry and Measurement
Geometry and Measurement
This domain tests plane and solid geometry vocabulary, angle relationships, perimeter, area, surface area, volume, coordinate geometry, and measurement conversions. Many items combine a formula with a unit conversion or a diagram described in words.
Core rules
- Angles: a straight angle is 180°, a full turn is 360°, and vertical angles are equal. Complementary angles sum to 90°; supplementary angles sum to 180°.
- Triangles have interior angles summing to 180°. The exterior angle equals the sum of the two remote interior angles. In any polygon with n sides, interior angles sum to (n − 2) × 180°.
- Perimeter is a length; area is measured in square units. Rectangle: A = lw. Triangle: A = ½bh. Circle: C = 2πr and A = πr².
- Volume is measured in cubic units. Rectangular prism: V = lwh. Cylinder: V = πr²h.
- Conversions: multiply by a conversion factor written as a fraction equal to 1. For square units, square the linear factor; for cubic units, cube it.
Worked example
A rectangular prism is 4 cm by 6 cm by 10 cm. Its volume is 4 × 6 × 10 = 240 cm³. Its surface area is 2(lw + lh + wh) = 2(24 + 40 + 60) = 2(124) = 248 cm². Volume counts cubic units inside; surface area counts square units covering all six faces.
Traps
Do not use diameter as radius in circle formulas. Do not confuse perimeter with area or report area in linear units. When converting square or cubic measures, do not apply the linear factor only once: 1 m² = 10,000 cm², and 1 m³ = 1,000,000 cm³. Check whether a question asks for a total, a missing angle, or a net.