Area Of A Trapezium

This interactive tool helps you understand and visualize the formula

It reveals a clever trick: any trapezium can be rearranged to form a rectangle where ½(a + b) is the base length of the rectangle

Grab and drag the four corner points (vertices) to create a trapezium of any size or shape you like. As you change the shape, all measurements update in real-time.

How to Use

General Controls

These controls are always visible and affect the entire canvas.

• Tools: Toggle the Ruler and Protractor to take measurements on the canvas.
• Randomize: Click the Randomize button to generate a new shape with different dimensions.
• Measurements: Use the Show Measurements button to toggle the visibility of length labels on the shape.
• Snap To: The Snap To dropdown changes how precisely you can drag the vertices, allowing you to snap to a grid or move freely.

Rectangle Tab ▭

This tab focuses on the properties of the transformed rectangle.

• Calculation Steps: Click the reveal buttons (base, height, formula, substitute, and area) to walk through the area calculation one step at a time.
• Toggle Grid: The Grid button fills the rectangle with unit squares to help visualize the area.
• Show Count: Once the grid is active, use the Show Count button to number the squares sequentially.

Trapezium Tab ⏢

This tab demonstrates the visual proof and area calculation for the trapezium.

• Calculation Steps: Step through the calculation using the reveal buttons for the top side (a), bottom side (b), height (h), the formula, and the final area.
• Animation Slider: The Animation slider is the key feature. Move it to watch the triangular ends of the trapezium rotate to form a perfect rectangle.
• Opacity Slider: Use the Background Opacity slider to adjust the transparency of the background rectangle during the animation.

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 Parallelogram is closely related to 3 other demonstrations that all use the area of a rectangle as a comparison:

• Area of a Rectangle
• Area of a parallelogram
• Area of a triangle