Area of a Triangle: A Visual Proof
This interactive demonstration allows you to explore the relationship between the area of a rectangle and the area of a triangle in a hands-on way. The demo visually illustrates that a triangle has exactly half the area of a rectangle that shares the same base and height. 📐
- Rectangle Area: Area = base × height
- Triangle Area: Area = ½ × base × height
Grab and drag the three markers to change the shape dimensions.
How to Use
Rectangle Tab ▭
This tab focuses on the basics of calculating a rectangle’s area.
- Reveal Buttons: Click the series of reveal buttons (▭ base, ▭ height, ▭ formula, and ▭ area) to walk through the calculation one step at a time.
- Toggle Grid: The Grid button overlays a grid of unit squares on the rectangle, helping you visualize and count the area.
- Show Count: Once the grid is active, use the Show Count button to number the squares sequentially, making it easy to verify the final area.
Triangle Tab △
This tab demonstrates the visual proof that a triangle’s area is half that of the corresponding rectangle.
- Reveal Buttons: Similar to the rectangle tab, you can step through the calculation using the reveal buttons for the △ base, △ height, △ formula, and △ area.
- Animation Slider: The Animation slider is the key feature here. Move it to watch the two halves of the triangle rotate 180° to the other half of the rectangle, providing a powerful visual proof of the area formula.
Global Controls
These controls are always visible and affect the entire canvas.
- Rulers: Toggle the Base Ruler and Height Ruler to measure the dimensions of the shapes on screen.
- Randomize: Click the Randomize button to generate a new problem with different dimensions.
- 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 to your liking.
- Paper Style: Use the Paper Style dropdown to change the background from plain to grid lines or dots.
- Paper Color: Pick a new Paper Color for the background.
- Line/Dot Color: Change the color of the background pattern with the Line/Dot Color picker.
Related Activities
Area of a Triangle is closely related to 3 other demonstrations that all use the area of a rectangle as a comparison: