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Triangle Calculator

Calculate triangle area and perimeter

Area

40.00 ft²

Perimeter

30.81 ft

Type

Right Scalene

Units
Right Scalene Triangle

Area

40.00

ft²

Perimeter

30.81

ft

Semi-Perimeter

15.40

ft

Sides

Side a

10.00

ft

Side b

8.00

ft

Side c

12.81

ft

Angles

Angle A

51.3°

Angle B

38.7°

Angle C

90°

Triangle Preview

A (51.3°)B (38.7°)C (90°)a = 10.0c = 12.8b = 8.0

Formulas Used

Triangle Area

Area = (base × height) / 2

The area of a triangle is half the product of its base and perpendicular height.

Where:

base= The base length of the triangle
height= The perpendicular height from base to opposite vertex

Triangle Perimeter (right triangle approximation)

Perimeter = base + height + √(base² + height²)

When only base and height are provided (no side lengths), the perimeter is estimated using a right triangle approximation.

Where:

base= The base length
height= The perpendicular height
√(base² + height²)= The hypotenuse (estimated third side)

Example Calculations

1Triangle: Base 10, Height 8

Inputs

Base10
Height8

Result

Area40.00
Perimeter30.81
Semi-Perimeter15.40

Area = (10 × 8) / 2 = 40.00. Perimeter (right triangle approx) = 10 + 8 + √(100 + 64) = 10 + 8 + 12.81 = 30.81. Semi-perimeter = 30.81 / 2 = 15.40.

2Triangle: Base 12, Height 5

Inputs

Base12
Height5

Result

Area30.00
Perimeter30.00
Semi-Perimeter15.00

Area = (12 × 5) / 2 = 30.00. Perimeter (right triangle approx) = 12 + 5 + √(144 + 25) = 12 + 5 + 13.00 = 30.00. Semi-perimeter = 30.00 / 2 = 15.00.

Frequently Asked Questions

Q

How do you calculate the area of a triangle?

Area of a triangle = (base × height) / 2. For example, a triangle with base 10 and height 8 has area = (10 × 8) / 2 = 40 square units. The height must be perpendicular to the base.

  • Formula: A = (base × height) / 2
  • Height must be perpendicular (90°) to the chosen base
  • Base 10, height 8: A = (10 × 8) / 2 = 40 square units
  • Any side can be the base — just use the matching perpendicular height
  • For right triangles: the two legs serve as base and height directly
Q

How do you calculate the perimeter of a triangle?

Perimeter = side1 + side2 + side3. Simply add all three side lengths. For a triangle with sides 5, 7, and 9, perimeter = 5 + 7 + 9 = 21 units.

  • Formula: P = a + b + c (sum of all three sides)
  • Equilateral triangle: P = 3 × side length
  • Isosceles triangle: P = 2 × equal side + base
  • Right triangle: if you know two sides, find the third with a² + b² = c²
  • Sides 5, 7, 9: P = 5 + 7 + 9 = 21 units
Q

What is the semi-perimeter of a triangle?

Semi-perimeter = (side1 + side2 + side3) / 2, or perimeter / 2. It's used in Heron's formula for calculating area when you know all three sides but not the height.

  • Formula: s = (a + b + c) / 2
  • Used as the key variable in Heron’s formula
  • Sides 5, 7, 9: s = (5 + 7 + 9) / 2 = 10.5
  • Also used in calculating the inradius: r = Area / s
  • Semi-perimeter is always greater than the longest side
Q

Can you calculate triangle area with only sides?

Yes, using Heron's formula: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter and a, b, c are the three sides. This works for any triangle when you know all three side lengths.

  • Heron’s formula: A = √[s(s–a)(s–b)(s–c)]
  • First calculate s = (a + b + c) / 2
  • Example: sides 3, 4, 5 → s = 6 → A = √(6×3×2×1) = √36 = 6
  • Works for ALL triangle types: acute, obtuse, and right
  • Alternative: use Law of Cosines to find an angle, then A = (1/2)ab×sin(C)
MethodRequired InputsBest When
Base × HeightBase + perpendicular heightHeight is known or easy to measure
Heron’s FormulaAll 3 side lengthsOnly sides are known, no angles
(1/2)ab sin(C)2 sides + included angleYou have an angle between two sides
Coordinate method3 vertex coordinates (x,y)Triangle defined on a coordinate plane

Understanding Triangle Calculations

A triangle's area is calculated using base and height: Area = (base × height) / 2. The height must be perpendicular to the base.

The perimeter is the sum of all three sides. The semi-perimeter is half the perimeter and is used in advanced formulas like Heron's formula.

For right triangles, you can use the Pythagorean theorem to find missing sides: a² + b² = c².

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Last Updated: Mar 26, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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