MathMe learning guide · Construction & measurement

Draw, constrain and measure 2D geometry

A geometric construction is more than a picture. Its rules describe what should remain true when you move a point.

Build a construction on the 2D board

Create a project and choose its 2D tab. Use Point, Line and Circle to make a simple construction. Snapping helps align a new point with existing points, midpoints, circles and the grid. A circle can be created by choosing its centre and setting a radius.

1. Draw a four-sided outline with connected corner points.
2. Add horizontal and vertical rules to the relevant edges.
3. Set one edge length and pin a point if you need an anchor.
4. Move another point and observe which relationships stay fixed.

Parallel and perpendicular rules describe relationships between lines. A fixed-length rule constrains a distance, while a fixed-radius rule constrains a circle. If rules conflict, the board marks the problem. Remove or adjust the conflicting rule rather than adding more constraints to force the picture into place.

Check a length with Pythagoras

Two points separated by a horizontal distance of 3 and a vertical distance of 4 are 5 units apart:

d = √((x₂ − x₁)² + (y₂ − y₁)²)
d = √(3² + 4²) = √25 = 5

Rotate the construction and measure again. Rotation changes the coordinate differences but preserves the distance. This is a useful way to separate a geometric property from the way a drawing sits on the screen.

Compare areas

A circle of radius 3 has area π × 3² = 9π, approximately 28.27 square units. Doubling its radius gives π × 6² = 36π: four times the area. Ask learners to predict that change before editing the radius.

For a simple closed polygon, the board can work through the shoelace formula using its ordered vertices. Keep the boundary connected and avoid crossing edges when you want to interpret the result as the area of one ordinary region.

Move from a region to a solid

A closed outline or circle can be extruded into a 3D object with a chosen height. For a straight extrusion, volume is base area multiplied by height. A rectangle with area 12 square units and an extrusion height of 5 has volume 60 cubic units.

This connection helps explain why area uses square units and volume uses cubic units. The original region measures two directions; the extrusion introduces a third. A line by itself has no enclosed area, so it is not the same starting point as a closed outline.

2D-to-3D conversion is a paid-plan feature in the hosted product. Review the plan comparison before planning an activity around it.

A reflection task

Make two different closed outlines with the same area. Extrude both to the same height. Predict their volumes, then compare the resulting shapes. Do equal volumes require equal surface areas? Describe what you measured and the assumptions you used.

Save the editable project for further work. Depending on your plan, SVG or DXF can carry a flat drawing to another tool, while PNG or PDF can support a written explanation. See the export guide for how file formats differ.