The shape atlas
Get to know the shapes.
Explore their properties, compare formulas, and try a calculation on every page.
2D · quadrilateral
Rectangle
A = w × h
Explore rectangle ↗2D · curved shapeCircle
A = πr²
Explore circle ↗2D · polygonTriangle
A = ½bh
Explore triangle ↗2D · quadrilateralTrapezoid
A = ½(a + b)h
Explore trapezoid ↗3D · curved solidSphere
V = ⁴⁄₃πr³
Explore sphere ↗3D · curved solidCylinder
V = πr²h
Explore cylinder ↗3D · curved solidCone
V = ⅓πr²h
Explore cone ↗3D · polyhedronRectangular prism
V = w × h × d
Explore rectangular prism ↗Compare the formulas
Use matching length units throughout. Area and surface area use squared units; volume uses cubed units.
| Shape | Measurement | Formula |
|---|---|---|
| Rectangle | Area | A = wh |
| Rectangle | Perimeter | P = 2(w + h) |
| Circle | Area | A = πr² |
| Circle | Circumference | C = 2πr |
| Triangle | Area | A = bh / 2 |
| Triangle | Perimeter | P = a + b + c |
| Trapezoid | Area | A = (a + b)h / 2 |
| Trapezoid | Midsegment | m = (a + b) / 2 |
| Sphere | Volume | V = 4πr³ / 3 |
| Sphere | Surface area | S = 4πr² |
| Cylinder | Volume | V = πr²h |
| Cylinder | Total surface area | S = 2πr² + 2πrh |
| Cone | Volume | V = πr²h / 3 |
| Cone | Total surface area | S = πr(r + ℓ) |
| Rectangular prism | Volume | V = whd |
| Rectangular prism | Surface area | S = 2(wh + wd + hd) |