Reference Formulas Guide

Review perimeter, area, and volume formulas for major geometric shapes.

Shape Name Type Perimeter / Circumference Area / Surface Area Volume Formula
Rectangle 2D Shape 2·(w + h) w · h —
Triangle 2D Shape a + b + c 0.5 · b · h —
Circle 2D Shape 2 · π · r π · r² —
Cuboid 3D Shape — 2·(lw + lh + wh) l · w · h
Cylinder 3D Shape — 2·π·r·(r + h) π · r² · h
Sphere 3D Shape — 4 · π · r² 4/3 · π · r³
Cone 3D Shape — π·r·(r + l) 1/3 · π · r² · h

Select any shape in the left navigation panel to access its interactive visualizer widget. Modify dimensions with sliders to view real-time projections and value evaluations.

Rectangle Simulator

Vary width and height and observe area scaling.

Adjust Dimensions
150 m
100 m
Rectangle Properties
Width (w): 150.0 m
Height (h): 100.0 m
Perimeter: 2·(w + h) 2 · (150.0 + 100.0) = 500.00 m
Area: w · h 150.0 * 100.0 = 15000.00 m²

Triangle Simulator

Adjust base and vertical height in a right-angled triangle.

Adjust Dimensions
160 m
120 m
Triangle Properties
Base (b): 160.0 m
Height (h): 120.0 m
Hypotenuse (c): 200.0 m
Perimeter: b + h + c 160 + 120 + 200 = 480.00 m
Area: 0.5 · b · h 0.5 * 160.0 * 120.0 = 9600.00 m²

Circle Simulator

Evaluate Area and Circumference properties.

Adjust Dimensions
90 m
Circle Properties
Radius (r): 90.0 m
Perimeter (2 · π · r): 2 * π * 90.0 = 565.49 m
Area (π · r²): π * 90.0² = 25446.90 m²

Cuboid (3D) Simulator

Interact with a rotating 3D wireframe cuboid and review formulas.

Adjust Dimensions
100 m
80 m
90 m
Cuboid 3D Properties
Dimensions (l×w×h): 100.0 × 80.0 × 90.0 m
Total Surface Area: 2·(lw+lh+wh) = 48400.00 m²
Volume (l · w · h): 100 * 80 * 90 = 720000.00 m³

Cylinder (3D) Simulator

Visualize volume and surface area properties of cylinders.

Adjust Dimensions
50 m
110 m
Cylinder 3D Properties
Radius (r): 50.0 m
Height (h): 110.0 m
Surface Area: 2πr(r+h) 50265.48 m²
Volume (π · r² · h): 863937.98 m³

Sphere (3D) Simulator

Evaluate spherical volume and shell area.

Adjust Dimensions
70 m
Sphere 3D Properties
Radius (r): 70.0 m
Surface Area (4 · π · r²): 61575.22 m²
Volume (4/3 · π · r³): 1436755.04 m³

Cone (3D) Simulator

Vary radius and vertical height to calculate slant height and volume.

Adjust Dimensions
50 m
100 m
Cone 3D Properties
Radius (r) | Height (h): 50.0 m | 100.0 m
Slant Height (l): 111.80 m
Surface Area (π·r·(r + l)): 25416.02 m²
Volume (1/3 · π · r² · h): 261799.39 m³

Geometry Practice Quiz

Identify shapes visually and match them with their respective formulas.

Question 1
Score: 0 / 0 🔥 Streak: 0