Geometry and Measurement
What Geometry and Measurement covers
This domain tests properties of 2-D and 3-D shapes, angle relationships, perimeter, area, volume, and conversion of units. You should know formulas and when each one applies, and be able to read a diagram’s labels without assuming lengths that are not marked.
Core rules
- Perimeter is the distance around a shape; add all side lengths. For a rectangle, P = 2(l + w).
- Area is measured in square units. Rectangle A = l × w; triangle A = ½ × base × height; parallelogram A = base × height.
- Volume is measured in cubic units. Cuboid V = l × w × h.
- Angles on a straight line total 180°; angles around a point total 360°; angles in a triangle total 180°.
- A right angle is 90°. Complementary angles total 90°; supplementary angles total 180°.
- Conversion: 1 m = 100 cm, 1 cm = 10 mm, 1 km = 1000 m; 1 kg = 1000 g; 1 L = 1000 mL. For area, linear conversions are squared (1 m² = 10,000 cm²); for volume, cubed.
Worked example
A triangle has base 12 cm and height 7 cm. Find its area. A = ½ × base × height = ½ × 12 × 7 = 6 × 7 = 42 cm². The height must be perpendicular to the base; a slanted side is not the height. If the same triangle’s sides are 12 cm, 8 cm, and 7 cm, its perimeter is 12 + 8 + 7 = 27 cm. Notice that perimeter is in cm, while area is in cm².
Traps that cost marks
Using diameter as radius: for a circle, r = d ÷ 2. Forgetting to halve when finding triangle area. Mixing units before calculating, such as adding 1.2 m to 35 cm without converting. Giving area in cm instead of cm², or volume in cm² instead of cm³. Assuming a diagram is drawn to scale-use the numbers, not the appearance. In angle problems, check whether angles form a straight line, a triangle, or a full turn before subtracting from 180° or 360°.