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.