Area and perimeter

Area and perimeter of plane shapes: circle, triangles, quadrilaterals, polygons, ellipse and land plots.

Pick a shape. Each calculator computes area and perimeter, draws the shape and shows the formulas.

Circle

S = πr²; o = 2πr

Area and circumference of a circle from radius or diameter.

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Triangle

S = a·vₐ/2; o = a+b+c

Area and perimeter of a general triangle.

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Right triangle

S = ab/2; c² = a²+b²

Area and perimeter of a right triangle.

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Equilateral triangle

S = (√3/4)a²; o = 3a

Area and perimeter of an equilateral triangle.

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Isosceles triangle

S = c·v/2; o = 2a+c

Area and perimeter of an isosceles triangle.

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Square

S = a²; o = 4a

Area and perimeter of a square.

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Rectangle

S = ab; o = 2(a+b)

Area and perimeter of a rectangle.

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Rhombus

S = a·v; o = 4a

Area and perimeter of a rhombus.

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Parallelogram

S = a·vₐ; o = 2(a+b)

Area and perimeter of a parallelogram.

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Trapezoid

S = (a+c)v/2; o = a+b+c+d

Area and perimeter of a trapezoid.

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Regular pentagon

S ≈ 1,720·a²; o = 5a

Area and perimeter of a regular pentagon.

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Regular hexagon

S = (3√3/2)a²; o = 6a

Area and perimeter of a regular hexagon.

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Regular polygon

S = (n·a²/4)·cot(180°/n); o = n·a

Area and perimeter of a regular n-gon.

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Pythagorean theorem

c² = a² + b²

Find the missing side of a right triangle.

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Annulus (ring)

S = π(R²−r²)

Area and perimeter of an annulus (ring).

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Circular sector

S = πr²·(α/360°)

Area and arc length of a circular sector.

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Circular segment

S = ½r²(α−sin α)

Area and chord of a circular segment.

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Ellipse

S = πab; o ≈ Ramanujan

Area and approximate perimeter of an ellipse.

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Kite (deltoid)

S = e·f/2; o = 2(a+b)

Area and perimeter of a kite.

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Land area from coordinates

S = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|

Area and perimeter of an irregular plot from vertex coordinates (shoelace formula).

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