Perimeter and Area Chapter Notes | Year 3 Mathematics IGCSE (Cambridge) - Class 3 PDF Download

Introduction

Imagine you're building a fence around your favorite park or coloring a picture within its lines! The concepts of perimeter and area help us understand the boundaries and space of shapes in a fun and practical way. In this chapter, we'll explore how to measure the distance around shapes (perimeter) and the space they cover (area). From fencing a garden to calculating the space on your desk, these ideas are like magic tools for everyday math adventures!

Perimeter

• Perimeter is the total distance around the boundary of a closed shape.
• It is found by adding up the lengths of all the sides of the shape.
• You can measure it using tools like a ruler, measuring tape, or even a rope!
• The word "perimeter" comes from Greek words meaning "around" and "measure."
• Example: Mr. Verma wants to fence his garden. He uses a rope, tying knots at each corner, and measures the total length as 20 meters. This 20 meters is the perimeter of his garden.

Finding Perimeter Using a Square Grid

• A square grid is made of small squares, each with a side of 1 cm.
• Draw the shape on the grid and count the number of unit lengths along its boundary.
• Add up these lengths to find the perimeter.
• Example: For a shape ABCDEFGH on a square grid (each square side is 1 cm), the perimeter is calculated as: AB = 3 cm, BC = 1 cm, CD = 1 cm, DE = 1 cm, EF = 2 cm, FG = 1 cm, GH = 4 cm, HA = 3 cm. Total = 3 + 1 + 1 + 1 + 2 + 1 + 4 + 3 = 16 cm.

Area

• Area is the amount of space inside the boundary of a closed shape.
• It is measured in square units, like square centimeters (sq. cm) or square meters (sq. m).
• You can find the area by covering the shape with unit squares and counting them.
• Example: A figure ABCD is made of 4 equal squares, each with an area of 1 square unit. The total area is 1 + 1 + 1 + 1 = 4 square units.

Finding Area by Counting Squares

• Place the shape on a square grid where each square has an area of 1 sq. cm.
• Trace the shape’s outline and count the number of squares it covers.
• The total number of squares gives the area in square units.
• Example: An eraser covers 8 complete squares on a grid where each square is 1 sq. cm. So, the area of the eraser is 8 × 1 sq. cm = 8 square centimeters.

Area of Irregular Plane Figures

• Irregular shapes don’t have a fixed shape, so we find their approximate area.
• Trace the shape on a square grid (each square = 1 square unit).
• Count squares as follows:
  • Whole squares covered = 1 square unit each.
  • Half squares covered = ½ square unit each.
  • Squares covered more than half = 1 square unit each.
  • Squares covered less than half = ignore them.
• Add up the areas to get the approximate total area.

Example: For an irregular shape:

• Whole squares = 4 (4 × 1 = 4 square units).
• Half squares = 2 (2 × ½ = 1 square unit).
• More than half squares = 2 (2 × 1 = 2 square units).
• Less than half squares = 4 (ignore).
• Total approximate area = 4 + 1 + 2 = 7 square units.