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Parallelogram Area and Properties

Sep 20, 2025

Overview

This lecture explains how to find the area of a parallelogram, highlights the correct use of the area formula, and provides example problems.

Properties of Parallelograms

  • A parallelogram is a quadrilateral (four-sided shape) with two pairs of parallel sides.
  • It resembles a rectangle but with slanted sides instead of square corners.

Parallelogram Area Formula

  • The area of a parallelogram is calculated as length × height (A = base × height).
  • This formula is the same as for rectangles, but the "height" must be perpendicular to the base.

Understanding Base and Height

  • The height is the perpendicular (straight up and down) distance between the bases, not the length of a slanted side.
  • If given a slanted side, do not use it as the height for the area formula.
  • The height may be shown as a dotted or imaginary line inside or outside the parallelogram.

Example Calculations

  • Example 1: For a parallelogram with base 6 inches and height 1.5 inches, area = 6 × 1.5 = 9 inches².
  • Example 2: For a parallelogram rotated 90 degrees, with length 5 inches and height 1.5 inches, area = 5 × 1.5 = 7.5 inches².
  • Example 3: For a parallelogram with base 10 cm and height 2 cm, area = 10 × 2 = 20 cm².

Key Terms & Definitions

  • Parallelogram — A quadrilateral with two pairs of parallel sides.
  • Base — Any side of a parallelogram chosen for measurement.
  • Height — The perpendicular distance from the base to the opposite side.
  • Area — The amount of space inside a shape, measured in square units (e.g., cm², in²).
  • Perimeter — The total distance around the sides of a shape.

Action Items / Next Steps

  • Practice finding the area of given parallelograms, ensuring you use the perpendicular height.
  • Review the difference between slanted sides and perpendicular height when identifying measurements.