Perimeter and Area of Polygons
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn how to calculate the perimeter and area of basic polygons and understand when to use each formula.
The Concept
Section titled “The Concept”Perimeter is the total distance around the outside of a polygon. It is found by adding the lengths of all sides.
Area is the amount of space inside the polygon. Different polygons have different area formulas.
Common formulas:
- Rectangle: Perimeter = 2(length + width). Area = length × width.
- Parallelogram: Perimeter = 2(base + side). Area = base × height (height is the perpendicular distance).
- Triangle: Perimeter = side₁ + side₂ + side₃. Area = ½ × base × height.
- Trapezoid: Perimeter = sum of all four sides. Area = ½ × (base₁ + base₂) × height.
Always make sure the height is the perpendicular distance (not the slanted side).
Worked Example
Section titled “Worked Example”-
Rectangle with length 8 cm and width 5 cm:
Perimeter = 2(8 + 5) = 26 cm
Area = 8 × 5 = 40 cm²
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Triangle with base 10 cm and height 6 cm:
Area = ½ × 10 × 6 = 30 cm²
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Trapezoid with bases 7 cm and 13 cm, height 5 cm:
Area = ½ × (7 + 13) × 5 = ½ × 20 × 5 = 50 cm²
Real-World Application
Section titled “Real-World Application”Perimeter and area are used constantly in everyday life:
- Perimeter: Fencing a yard, framing a picture, measuring the border of a room for baseboard or crown molding.
- Area: Buying paint or carpet (how much floor space), calculating lawn fertilizer, determining how much wallpaper or tile you need.
For example: A rectangular garden is 12 feet by 8 feet. Perimeter tells you how much fencing you need: 2(12 + 8) = 40 feet. Area tells you how much soil or seed you need: 12 × 8 = 96 square feet.