Geometry and Measurement
Geometry and Measurement asks you to classify two-dimensional figures, reason about angles, compute perimeter, area, and volume, and convert among units. Diagrams are usually described in words, so you must build the figure from the given measurements.
Figures and angles
- Triangles by sides: equilateral has three equal sides; isosceles has at least two equal sides; scalene has no equal sides. By angles: acute, right, or obtuse.
- Quadrilateral hierarchy: a square is a rectangle and a rhombus; rectangles and rhombuses are parallelograms.
- Angles: acute is less than 90°, right is 90°, obtuse is between 90° and 180°, and straight is 180°.
- The angles of a triangle sum to 180°; the angles of a quadrilateral sum to 360°.
Perimeter and area
- Perimeter is the distance around a figure; add side lengths and use linear units.
- Rectangle area = length × width; parallelogram area = base × height; triangle area = 1/2 × base × height.
- Composite figures: decompose into rectangles or triangles and add areas, or subtract a cutout from a larger shape.
Volume
- Rectangular prism volume = length × width × height, in cubic units.
- Volume measures space inside; surface area measures covering outside. Do not interchange them.
Units
- 1 m = 100 cm; 1 km = 1000 m; 1 kg = 1000 g; 1 L = 1000 mL; 1 cm³ = 1 mL.
- Convert by multiplying or dividing and keep the unit labels.
Worked example
An L-shaped figure is made from an 8 cm by 5 cm rectangle plus a triangle with base 8 cm and height 3 cm. Rectangle area = 8 × 5 = 40 cm². Triangle area = 1/2 × 8 × 3 = 12 cm². Total area = 52 cm². The perimeter is not 52 cm; it requires adding every outer side.
Traps that cost marks
- Confusing perimeter with area.
- Forgetting the factor of 1/2 in a triangle’s area.
- Mixing centimetres and metres without converting.
- Reporting volume when the question asks for surface area, or the reverse.
- Assuming every rhombus is a square.