Area of a Parallelogram: A Visual Proof
This interactive demo visually explains why the formula for the area of a parallelogram is Area = base × height. It demonstrates the powerful idea that any parallelogram can be rearranged into a rectangle that has the exact same base, height, and total area. 🧐
Grab and drag the three markers to change the shape’s dimensions and explore this concept for yourself. By experimenting with the tool, you’ll gain an intuitive understanding that the slant of the sides doesn’t change the area, as long as the base and perpendicular height remain constant.
How to Use
Rectangle Tab ▭
This tab helps you understand the area of a rectangle, which is the foundation for the parallelogram’s area.
- Step-by-Step Calculation: Click the series of reveal buttons to walk through the calculation: ▭ base, ▭ height, ▭ formula, ▭ substitute, and finally the ▭ area.
- Visualize Area: Use the Grid button to overlay a grid of unit squares. Then, use the Show Count button to number the squares and easily verify the area calculation.
Parallelogram Tab ▱
This tab contains the visual proof for the parallelogram’s area formula.
- Step-by-Step Calculation: Just like the rectangle tab, you can reveal the ▱ base, ▱ height, ▱ formula, ▱ substitute, and the final ▱ area.
- Animation Slider: This is the key feature! Move the Animation slider to watch the triangle pieces rotate from one side to the other, transforming the parallelogram into a rectangle.
- Background Shape: Use the Background Opacity slider to see the final rectangular shape that the parallelogram transforms into.
Global Controls
These controls are always available at the bottom of the sidebar.
- Practice Problems: Click the Randomize button to generate a new shape. Use the Problem Type dropdown to choose whether you want to find the area, base, or height.
- Measurement Tools: Toggle the Ruler, Protractor, and Measurement Labels to get more information about the shape.
- Snap To: The Snap To dropdown changes how precisely you can drag the vertices, allowing you to snap to full, half, or quarter units.
Settings Tab ⚙️
Customize the look of the canvas.
- Paper Style: Use the Paper Style dropdown to change the background from plain to grid lines or dots.
- Colors: Use the color pickers to change the Paper Color, Line/Dot Color, shape Fill Color, and Outline Color.
Related Activities
Area of a Parallelogram is closely related to 3 other demonstrations that all use the area of a rectangle as a comparison: