Drag the sliders to see how rectangles, triangles, parallelograms, rhombi and trapeziums build up their area formulas — and why the perimeter never tells the whole story.
Area is the number of unit squares that pack a region. For a rectangle, that number is simply length × width. Drag the sliders and watch the unit-square grid.
Two rectangles can share the same perimeter yet have very different areas. Adjust each rectangle independently and compare.
A triangle enclosed in a rectangle always fills exactly half of it. Drag the vertex along the top and change the base/height to see the ½ × base × height rule hold every time — even for obtuse triangles.
Cut a triangular piece off one end of a parallelogram and slide it to the other end — it becomes a rectangle of the very same area. Press "Dissect" to watch it happen.
A rhombus's diagonals are perpendicular bisectors of each other. That lets us split it into 4 right triangles that can be rearranged into a rectangle of sides d₁ and d₂⁄2.
Split the trapezium into a rectangle and two triangles, or picture two copies joined to form a parallelogram. Either way, the area comes out to half the height times the sum of the parallel sides.
Any polygon — quadrilateral, pentagon, hexagon — can be divided into triangles from one chosen vertex. Once we know each triangle's area, we can add them up to get the whole polygon's area. Choose the number of sides and see the triangulation.
1 in = 2.54 cm, so a 1 in × 1 in square equals a 2.54 cm × 2.54 cm square — that's 2.54² = 6.4516 cm² per square inch. Try converting either way below.