Geometry and Measurement
What this domain tests
Geometry and measurement items test angle relationships, triangle properties, perimeter and area, circles, volume and surface area, similarity, coordinate geometry, and unit conversion. Formulas are straightforward; marks are lost by using the wrong dimension or forgetting units.
Core rules
- Angles on a line sum to 180 degrees; angles around a point sum to 360 degrees. Vertical angles are equal.
- Triangle angles sum to 180 degrees. In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse.
- Area of a triangle = 1/2 bh; rectangle = lw; circle = pi r^2. Circumference = 2 pi r.
- Volume of a rectangular prism = lwh; cylinder = pi r^2 h. Surface area is the sum of all face areas.
- Similar figures have equal angles and proportional sides. If the scale factor is k, areas scale by k^2 and volumes by k^3.
- Distance between points = square root of [(x2 - x1)^2 + (y2 - y1)^2]; midpoint averages the coordinates.
Worked example
A right triangle has legs 9 and 12. The hypotenuse is the square root of (81 + 144) = square root of 225 = 15. Its area is 1/2 x 9 x 12 = 54 square units. The perimeter is 9 + 12 + 15 = 36 units. Area uses the two legs, not the hypotenuse, and is reported in square units.
Traps
Diameter is twice the radius; using diameter in pi r^2 quadruples the area. Slant height and perpendicular height are different in cones and pyramids. Convert units before multiplying: 1 m = 100 cm, so 1 m^2 = 10,000 cm^2. When a figure is enlarged by a scale factor, do not multiply the area by the same factor; multiply by its square.