Shape and Space: Measurement, Area, Volume, and Geometry
What you must understand
Shape and space covers measurement units and conversions, perimeter, area of rectangles, triangles, and parallelograms, volume of rectangular prisms, angle relationships, and properties of two- and three-dimensional figures. You should know that the area of a triangle is half the base times the height, that the area of a parallelogram is base times height, and that volume of a prism is the area of its base times its height. Angle facts include the straight-line sum of 180 degrees and the full-turn sum of 360 degrees. You must also convert among metric units and between common time units.
Traps to watch for
- Height versus slant side: for triangles and parallelograms, the height is perpendicular to the base, not the slanted edge.
- Mixing units: convert to a common unit before multiplying; area units are squared and volume units are cubed, so 1 square metre is 10 000 square centimetres, not 100.
- Perimeter versus area: perimeter is a length in linear units; area is in square units.
- Volume of a prism: multiply the base area by the height, and do not confuse it with surface area.
- Angle reasoning: complementary angles total 90 degrees, supplementary angles total 180 degrees, and vertically opposite angles are equal.
Worked example
A triangular garden has a base of 12 m and a perpendicular height of 7 m. Area = (base × height) ÷ 2 = (12 × 7) ÷ 2 = 84 ÷ 2 = 42 square metres. If a rectangular prism has a base of 5 cm by 4 cm and a height of 3 cm, its base area is 20 square centimetres and its volume is 20 × 3 = 60 cubic centimetres.
Rule of thumb
Label every measurement with its unit, convert to one unit before calculating, and ask whether the answer should be linear, squared, or cubed.