Area Lab
Move the sliders and watch the geometry respond. Dissect a triangle out of its rectangle, shear a parallelogram
without changing its area, and grow a circle — the formulas stop being memorization and start being obvious.
1 · The triangle is half its rectangle
Drag the apex along the top edge. The blue triangle always fills exactly half of the dashed rectangle.
Rectangle
60
Triangle
30
Ratio
1/2
2 · Shear the parallelogram
Slide it sideways. The base and the vertical height never change — so the area never changes either.
Base
8
Height
5
Area
40
3 · Grow the circle
Grow the radius and watch the area grow with the square of the radius — that is why the formula is πr², not πr.
Radius
3
Exact area
9π
Decimal
28.27
Challenges
Set the sliders, then press Check.