Area and Perimeter Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download

Estimating and measuring area and perimeter

• The objective is to estimate and measure the perimeter of 2D shapes.
• Use appropriate units (mm, cm, m, km) to record perimeter measurements.
• Record area using square units (mm², cm², m², km²).
• Estimate the area of shapes by counting whole and partial squares.
• Add the areas of different shapes to find the total area.
• Perimeter:
  • The perimeter is the total length of the boundary of a 2D shape, calculated by summing the lengths of all sides.
  • Units are chosen based on the shape’s size, e.g., mm for small objects like stamps, m for rooms, km for large areas like theme parks.
  • Conversions between units: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
  • Example: A playground with sides 1 m, 8 m, 10 m, 10 m requires calculating the perimeter to determine fencing needs.
• Area:
  • Area measures the surface enclosed by a shape, recorded in square units (mm², cm², m², km²) based on the object’s scale, e.g., mm² for a drop of water, km² for a sea.
  • Estimation involves counting whole squares and squares more than half-covered, e.g., for a juice spill covering 10 whole squares and 6 more-than-half-covered squares, the estimated area is 16 cm² if each square is 1 cm × 1 cm.
  • Total area of composite shapes is found by adding the areas of individual shapes.
• Accurate estimation and measurement are crucial for practical applications, such as determining materials needed for tiling or fencing.

Area and perimeter of rectangles

• The objective is to draw rectangles and calculate their area and perimeter.
• Investigate methods to calculate the area of rectangles efficiently.
• Add the areas of multiple rectangles to find the total area of composite shapes.
• Perimeter of a rectangle:
  • Calculated by summing all side lengths: perimeter = side1 + side2 + side3 + side4.
  • For a rectangle with opposite sides equal (e.g., 3 cm, 4 cm, 3 cm, 4 cm), perimeter is 3 + 4 + 3 + 4 = 14 cm.
  • Alternatively, perimeter can be calculated as 2 × (length + width), e.g., for a rectangle with length 4 cm and width 3 cm, 2 × (4 + 3) = 14 cm.
• Area of a rectangle:
  • Area is calculated by counting the number of square units enclosed, e.g., a rectangle with 3 rows of 4 squares has an area of 3 × 4 = 12 cm² if each square is 1 cm × 1 cm.
  • Formula: area = length × width, e.g., for a rectangle with length 8 cm and width 3 cm, area = 8 × 3 = 24 cm².
  • Counting in rows or columns simplifies calculation, e.g., 5 squares/row × 3 rows = 15 cm².
• Composite shapes:
  • The total area of a shape made of multiple rectangles is the sum of the individual rectangle areas.
  • Example: A floor plan with a hall and office requires adding the areas of each rectangular section.
• Applications include calculating materials for floor coverings, where areas are measured in square units to determine quantities needed.