Geometry, Measurement & Data
Measurement: Area, Perimeter, Volume, and Angles
Grade 4 · Grade 5 · Grade 6
- ✓By the end of this lesson students will be able to calculate the perimeter of various polygons.
- ✓By the end of this lesson students will be able to calculate the area of rectangles and squares.
- ✓By the end of this lesson students will be able to calculate the volume of rectangular prisms.
- ✓By the end of this lesson students will be able to identify and classify different types of angles (acute, right, obtuse, straight).
- ✓By the end of this lesson students will be able to measure angles using a protractor.
Key concepts
Perimeter is the total distance around the outside edge of a two-dimensional (2D) shape. To find the perimeter, you add up the lengths of all its sides.
Area is the amount of surface a two-dimensional (2D) shape covers. It is measured in square units (e.g., square centimetres, square metres).
Volume is the amount of space a three-dimensional (3D) object occupies. It is measured in cubic units (e.g., cubic centimetres, cubic metres).
An angle is formed when two rays meet at a common point called a vertex. Angles are measured in degrees (°). There are different types of angles:\n- Acute angle: Less than 90°.\n- Right angle: Exactly 90° (often shown with a small square symbol).\n- Obtuse angle: Greater than 90° but less than 180°.\n- Straight angle: Exactly 180° (forms a straight line).
Key facts to remember
- 1Perimeter is the distance around a 2D shape, measured in linear units (e.g., cm, m).
- 2Area is the amount of surface a 2D shape covers, measured in square units (e.g., cm², m²).
- 3Volume is the amount of space a 3D object occupies, measured in cubic units (e.g., cm³, m³).
- 4An acute angle is less than 90°.
- 5A right angle is exactly 90°.
- 6An obtuse angle is greater than 90° but less than 180°.
- 7A straight angle is exactly 180°.
- 8A protractor is used to measure angles.
Worked examples
Example 1
A rectangular playground is 15 metres long and 10 metres wide. Calculate its perimeter and area.
Answer
The perimeter of the playground is 50 m. The area of the playground is 150 m².
Remember to use the correct units: metres (m) for perimeter and square metres (m²) for area.
Example 2
A storage box is 50 cm long, 20 cm wide, and 30 cm high. What is the volume of the storage box?
Answer
The volume of the storage box is 30 000 cm³.
Volume is always measured in cubic units (e.g., cm³).
Example 3
Identify the type of angle shown and state its measure if it is 135 degrees.
Answer
The angle is an obtuse angle, measuring 135°.
To measure an angle with a protractor, place the centre of the protractor on the vertex of the angle and one arm of the angle along the 0° line. Read the measure where the other arm crosses the scale.
Common mistakes
- ✗Confusing perimeter and area, or using the wrong formula for each.
- ✗Using incorrect units for perimeter (e.g., cm²) or area (e.g., cm).
- ✗Forgetting to add all side lengths when calculating the perimeter of irregular shapes.
- ✗Incorrectly reading a protractor, especially when there are two scales.
- ✗Mixing up the dimensions (length, width, height) when calculating volume.
Exam tips
- ★Always write down the correct formula before substituting numbers.
- ★Double-check your calculations and make sure your answer includes the correct units.
- ★If a diagram is not provided, draw one to help visualize the problem.
- ★When using a protractor, ensure the centre mark is on the angle's vertex and one arm aligns with the 0° line.
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