Triangle Area and Perimeter Calculator

Free online Triangle Area and Perimeter Calculator that runs directly in your browser.

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Result

raw: Sides: a=3, b=4, c=5 Perimeter (P): 12 Area (A): 6 Type: Scalene Right triangle: Yes Steps: s = P/2 = 12/2 = 6 A = √(s(s−a)(s−b)(s−c)) A = √(6(6-3)(6-4)(6-5))

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Triangle area and perimeter calculator - all formulas

A triangle is a basic geometric figure with three sides and three angles adding up to 180°. The calculator calculates the area (Heron's formula, 1/2bh), perimeter, missing sides/angles (law of cosines, sines) and classifies the type of triangle.

triangle area calculator triangle perimeter Heron's formula triangle calculations calculator

Triangle area formulas

Area = (base × height) / 2. Heron's formula: s=(a+b+c)/2; P = √(s×(s-a)×(s-b)×(s-c)). Two sides and the angle between them: P = (1/2) × a × b × sin(C). Equilateral triangle: P = (√3/4) × a². Right triangle: P = (1/2) × side1 × side2.

Calculating missing elements

Law of cosines: c² = a² + b² - 2ab×cos(C). The law of sines: a/sin(A) = b/sin(B) = c/sin(C). Sum of angles: A + B + C = 180°. Missing side of 2 sides and an angle: use the law of cosines. Missing angle from 3 sides: arccos((a²+b²-c²)/(2ab)).

Types of triangles

Acute: all angles < 90°. Rectangular: one angle = 90° (Pythagoras: a²+b²=c²). Obtuse: one angle > 90°. Equilateral: a=b=c, all angles=60°. Isosceles: two sides are equal. Variable: all sides different. Check: rectangular if a²+b²=c² (for c=hypotenuse).

Height of the triangle

Height h_a (on side a): h_a = 2P/a (where P = area). For a right triangle: h into hypotenuse c: h = (a×b)/c. Trace points: orthocentre = point of intersection of heights. Inside for the acute angle, outside for the obtuse angle, at the vertex for the right angle.

Frequently asked questions

How to calculate the area of a triangle knowing 3 sides?

Heron's formula: s = (a+b+c)/2. P = sqrt(s(s-a)(s-b)(s-c)). Example: a=3, b=4, c=5. s=6. P=sqrt(6×3×2×1)=sqrt(36)=6. Check: 3-4-5 is a right triangle, P=(3×4)/2=6 ✓. Calculator: enter 3 sides and click calculate.

How to check if 3 sides form a triangle?

Triangle inequality: each side < the sum of the other two. a < b+c, b < a+c, c < a+b. Example: 3,4,5 → 3<9, 4<8, 5<7 ✓. Counterexample: 1,2,10 → 10 < 1+2=3 ✗ (not a triangle). Equality (degenerate triangle): a=b+c → segment, not triangle.

Pythagorean Theorem - Applications

c² = a² + b² (right triangle). Checking the right angle: 3²+4²=5² → 9+16=25 ✓. Diagonal of the rectangle: d=√(a²+b²). Point distance: d=√((x2-x1)²+(y2-y1)²). Pythagorean triangles: 3-4-5, 5-12-13, 8-15-17, 7-24-25.

How does the calculator calculate side angles?

Law of cosines: A = arccos((b²+c²-a²)/(2bc)). When we know a,b,c: calculate A, B, then C = 180°-A-B. JavaScript: Math.acos((b*b+c*c-a*a)/(2*b*c)) * (180/Math.PI) = degrees. Check: A+B+C should = 180°.

What is Pascal's triangle and what does it have to do with a geometric triangle?

Pascal's triangle: matrix of binomial coefficients (1, 1 1, 1 2 1, ...). Built by adding adjacent elements. Geometry: Sierpinski triangle (fractal) can be obtained from Pascal's triangle (mod 2). Mathematically: "Pascal's triangle" and "geometric triangle" are completely different concepts - only the name connects them.

Related tools: right triangle calculator, area calculator and vector calculator.