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 shape

Circle

A = πr²

Explore circle ↗
2D · polygon

Triangle

A = ½bh

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2D · quadrilateral

Trapezoid

A = ½(a + b)h

Explore trapezoid ↗
3D · curved solid

Sphere

V = ⁴⁄₃πr³

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3D · curved solid

Cylinder

V = πr²h

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3D · curved solid

Cone

V = ⅓πr²h

Explore cone ↗
3D · polyhedron

Rectangular 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.

ShapeMeasurementFormula
RectangleAreaA = wh
RectanglePerimeterP = 2(w + h)
CircleAreaA = πr²
CircleCircumferenceC = 2πr
TriangleAreaA = bh / 2
TrianglePerimeterP = a + b + c
TrapezoidAreaA = (a + b)h / 2
TrapezoidMidsegmentm = (a + b) / 2
SphereVolumeV = 4πr³ / 3
SphereSurface areaS = 4πr²
CylinderVolumeV = πr²h
CylinderTotal surface areaS = 2πr² + 2πrh
ConeVolumeV = πr²h / 3
ConeTotal surface areaS = πr(r + ℓ)
Rectangular prismVolumeV = whd
Rectangular prismSurface areaS = 2(wh + wd + hd)