Perimeter and Area

6.1 Perimeter

The concept of perimeter refers to the total distance around the boundary of a closed plane figure. When you walk along the edges of a shape and return to the starting point, the distance covered is the perimeter. This applies to all closed shapes, including polygons, which are figures made up of straight line segments. The perimeter of a polygon is the sum of the lengths of all its sides. Understanding perimeter is fundamental in geometry and has practical applications such as fencing a field, framing a picture, or laying borders around gardens. For polygons, since the sides are line segments, measuring each side and adding them gives the perimeter. This chapter revisits the formulas for the perimeter of common polygons like rectangles, squares, and triangles, helping students understand how to calculate the perimeter efficiently.

• Perimeter is the total distance around a closed plane figure.
• For polygons, perimeter equals the sum of the lengths of all sides.
• Understanding perimeter helps in real-life tasks like fencing and framing.
• Polygons are closed figures made of line segments.
• Formulas for perimeter simplify calculations for regular shapes.
• Perimeter is measured in linear units such as cm, m, etc.
• 📌 Perimeter: Total distance around the boundary of a closed figure.
• 📌 Polygon: A closed plane figure made up of line segments.

Perimeter of a rectangle

A rectangle is a four-sided polygon with opposite sides equal and all angles right angles. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides are equal, the perimeter can be simplified to twice the sum of the length and breadth. For example, consider a rectangle ABCD with length 12 cm and breadth 8 cm. The perimeter is calculated as AB + BC + CD + DA. Since AB = CD = 12 cm and BC = DA = 8 cm, the perimeter equals 2 × (length + breadth) = 2 × (12 cm + 8 cm) = 40 cm. This formula is efficient and widely used for calculating the perimeter of rectangles.

• Rectangle has opposite sides equal in length.
• Perimeter of rectangle = sum of all four sides.
• Simplified formula: Perimeter = 2 × (length + breadth).
• Example: Rectangle with length 12 cm and breadth 8 cm has perimeter 40 cm.
• Useful for calculating fencing or borders around rectangular areas.
• Units of perimeter are linear (e.g., cm, m).
• 📌 Length: Longer side of a rectangle.
• 📌 Breadth: Shorter side of a rectangle.
• 📌 Perimeter: Total distance around the rectangle.