2D shape area and perimeter calculator for every common figure. Useful for students and professionals.
Six tabs covering: square and rectangle, triangle, circle, trapezoid, rhombus and parallelogram, and regular n-gons. Each tab includes the formula and a visualization.
Calculator information
📋 How to use this calculator
- Choose the 2D shape to compute: square, rectangle, triangle, circle, trapezoid, rhombus, parallelogram, or regular n-gon.
- Enter the dimensions appropriate to the shape: side for square; length and width for rectangle; radius for circle; parallel sides and height for trapezoid.
- Keep all units consistent (cm, m, or inch); the calculator returns area in square units and perimeter in linear units.
- For triangles, choose a method: base-height if known, Heron's formula for all three sides, or two sides plus included angle for the trigonometric formula.
- View the area, perimeter, and a visualization of the shape with the entered dimensions.
- Tip: for irregular shapes, split them into several regular shapes, compute each, then sum the results.
🧮 Area and Perimeter Formulas for 2D Shapes
Square: A = s^2, P = 4s | Rectangle: A = l x w, P = 2(l+w) | Triangle: A = (b x h)/2 | Circle: A = pi x r^2, C = 2 x pi x r | Trapezoid: A = ((a+b) x h)/2 | Rhombus: A = (d1 x d2)/2 | Parallelogram: A = b x h | Regular n-gon: A = (n x s^2)/(4 x tan(pi/n))
- s = side length (cm/m)
- l, w = length and width of rectangle
- b, h = base and height
- r = circle radius
- pi = 3.14159265... (circle constant)
- d1, d2 = rhombus diagonals
- n = number of sides of a regular polygon
All formulas assume regular shapes. For irregular shapes, use decomposition or numerical integration. Area units are always squared (cm^2, m^2, etc.).
💡 Worked example: Computing the area of a trapezoid and a circle
Given:- Trapezoid: parallel sides a = 8 cm, b = 12 cm, height h = 5 cm
- Circle: radius r = 7 cm
- Find the area and perimeter of each
Steps:- Trapezoid area: A = ((8 + 12) x 5) / 2 = (20 x 5) / 2 = 100/2 = 50 cm^2
- Trapezoid perimeter needs the slant length; for an isosceles trapezoid with a 4 cm difference between the parallel sides, slant = sqrt(2^2 + 5^2) = sqrt(29) = 5.39 cm
- Trapezoid perimeter: 8 + 12 + 5.39 + 5.39 = 30.78 cm
- Circle area: A = pi x 7^2 = 3.14159 x 49 = 153.94 cm^2
- Circle circumference: C = 2 x 3.14159 x 7 = 43.98 cm
Result: Trapezoid: area 50 cm^2, perimeter 30.78 cm. Circle: area 153.94 cm^2, circumference 43.98 cm.
❓ Frequently asked questions
What is the difference between area and perimeter?
Area is the measure of the region covered by a 2D shape (a 2-dimensional quantity in squared units such as cm^2 or m^2), while perimeter is the sum of the lengths of all sides or the length of the boundary path (a 1-dimensional quantity in linear units such as cm or m). For example, a 5x4 meter garden has an area of 20 m^2 (paving tile coverage) and a perimeter of 18 m (fence length).
Why do circle formulas use pi?
Pi (pi = 3.14159...) is the constant ratio of a circle's circumference to its diameter, true for every circle regardless of size. This constant has been known since Babylonian times (around 2000 BCE) and was rigorously bounded by Archimedes using polygons. Pi is irrational and transcendental, meaning it cannot be expressed as a simple fraction and has non-repeating decimals.
How do I compute the area of an irregular shape?
Irregular shapes can be tackled by decomposition (splitting into several regular shapes such as squares, triangles, or trapezoids and summing their areas), by the grid method (counting covered unit squares), or by calculus integration for curved shapes. For maps or digital images, tools such as AutoCAD or GIS can compute area automatically from boundary coordinates.
What is a regular n-gon and how do I compute its area?
A regular n-gon is a polygon with n sides all equal in length and all interior angles equal. Examples: equilateral triangle (n=3), square (n=4), pentagon (n=5), hexagon (n=6). Area formula: A = (n x s^2) / (4 x tan(pi/n)), where s is the side length. The more sides, the closer the shape gets to a circle whose radius equals the distance from center to vertex.
When do I use base-height vs Heron's formula for triangles?
Use A = (base x height) / 2 when the triangle's height (perpendicular from a vertex to the base) is known or easily found, as with right or isosceles triangles. Use Heron's formula A = sqrt(s(s-a)(s-b)(s-c)) when only the three sides are known and height is hard to determine. For a triangle with two sides and the included angle, use A = (a x b x sin(C))/2.
📚 Sources & references
Last updated: May 11, 2026