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Triangle Area Calculator

Introduction

Welcome to our Triangle Area Calculator! which will help you calculate the triangle’s area quickly and accurately. A triangle is a polygon with three sides and three angles. The shape is formed when three straight lines meet. The point at which the lines meet is called a vertex, and a triangle has three vertices.

The area of the triangle is defined as the space within the triangle’s three sides. So, it depends on the length of the sides and the internal angles of the triangle.

How to use the Triangle Area Calculator?

Using the Triangle Area Calculator you can calculate the area of the triangle using multiple methods

We can calculate the area of triangle using the following methods

  1. Area of Triangle using Basic Formula
  2. Area of Triangle using Heron’s Formula
  3. Area of Triangle using Two Sides and Included Angle (SAS) Formula
  4. Area of Equilateral Triangle Formula
  5. Area of Isosceles Triangle Formula

Area of Triangle using Basic Formula

The variables in the Triangle Area Calculator include:

Base (b)
The length of the base of the triangle.

Height (h)
The length of the triangle’s altitude is the perpendicular drawn from the vertex to the opposite side.

Triangle Area (A)
We can calculate the area of the triangle using the following formula.

Area=12×Base×Perpendicular Height\text{Area} = \normalsize \dfrac{1}{2} \times \text{Base} \times \text{Perpendicular Height}

Area of Triangle using Heron’s Formula

We can also calculate the area of the triangle using Heron’s Formula. We use this formula when we want to calculate the area of the triangle using the length of the three sides.

The variables in the Triangle Area Calculator include:

1st Side (a):
Length of 1st Side

2nd Side (b):
Length of 2nd Side

3rd Side (c):
Length of 3rd Side

Triangle Area (A)
We can calculate the area of the triangle using the following formula.

s=a+b+c2A=s(s−a)(s−b)(s−c)\begin{aligned} s &= \normalsize \dfrac{a + b + c}{2} \\[10pt]A &= \sqrt{s(s-a)(s-b)(s-c)}\end{aligned}

Where,

s = Semi-perimeter of the triangle

Area of Triangle using Two Sides and Included Angle (SAS) Formula

We can also calculate the area of a triangle when we have the length of two sides and the included angle of the triangle.

The variables in the Triangle Area Calculator are:

Side 1 (a)
Length of one side of the Triangle

Side 2 (b)
Length of the second side of the Triangle

Included Angle (A)
The angle between Side 1 (a) and Side 2 (b) is in degrees.

Triangle Area (S)
We can calculate the area of the triangle using the following formula.

Area=12×ab×sin(A)\text{Area} = \normalsize \dfrac{1}{2} \times ab \times sin(A)

Area of Equilateral Triangle Formula

We can also calculate the area of the equilateral triangle, where all sides are equal.

The variables in the Triangle Area Calculator include:

Length of Side (a) The length of a side of an equilateral triangle.

Area of the Equilateral Triangle (Area) We can calculate the area of the equilateral triangle using the following formula

Area=34×a2\text{Area} = \normalsize \dfrac{\sqrt{3}}{4} \times a^2

Area of Isosceles Triangle Formula

We can also calculate the area of an Isosceles Triangle, which has two sides equal.

The variables in the Triangle Area Calculator include

Base (b) The length of the base of the triangle.

Equal Side Length (a) The length of one of the equal sides.

Area of a triangle (Area) The area of the triangle is calculated using the formula

Area=14×b×4a2−b2\text{Area} = \normalsize \dfrac{1}{4} \times b \times \sqrt{4a^2 - b^2}

What is a Triangle?

A triangle is a 2-dimensional shape with three sides, it also has three interior angles and three vertices. The sum of the internal angles will always be equal to 180 degrees.

Basically, triangles can be classified based on the length of their sides or based on their angles.

Based on the Length of the Sides

  1. Equilateral Triangle: when all sides are equal.
  2. Isosceles Triangle: when two sides are equal.
  3. Scalene Triangle: when no side is equal.

Based on the Angles

  1. Acute Triangle: has all angles less than 90 degrees.
  2. Right Angle Triangle: one angle is equal to 90 degrees.
  3. Obtuse Triangle: one angle is greater than 90 degrees.

How is the Area of the Triangle Calculated?

The area of the triangle can be calculated using multiple methods as shown below.

Area of Triangle using Basic Formula

You can calculate the area of the triangle by using the basic formula, where we require the base and the perpendicular height of the triangle to calculate the area.

Area=12×Base×Perpendicular Height\text{Area} = \normalsize \dfrac{1}{2} \times \text{Base} \times \text{Perpendicular Height}

Area of Triangle using Heron’s Formula

You could also calculate the area of the triangle by using Heron’s formula. This formula is used when we have all the sides of the triangle and we need to calculate the area.

s=a+b+c2A=s(s−a)(s−b)(s−c)\begin{aligned} s &= \normalsize \dfrac{a + b + c}{2} \\[10pt]A &= \sqrt{s(s-a)(s-b)(s-c)} \end{aligned}

Where,

s = Semi-perimeter of the triangle

Area of Triangle using Two Sides and Included Angle (SAS) Formula

Another method for calculating the area of the triangle when we have two sides of the triangle and the included angle is called the SAS method. You could use the following formula to calculate the area.

Area=12×ab×sin(A)\text{Area} = \normalsize \dfrac{1}{2} \times ab \times sin(A)

Where,

a = 1st Side of the Triangle

b = 2nd Side of the Triangle

A = Included angle between a and b

Area of Equilateral Triangle Formula

Area=34×a2\text{Area} = \normalsize \dfrac{\sqrt{3}}{4} \times a^2

Where,

a = Side of the equilateral triangle

Area of Isosceles Triangle Formula

Area=14×b×4a2−b2\text{Area} = \normalsize \dfrac{1}{4} \times b \times \sqrt{4a^2 - b^2}

Where,

b = base of the triangle

a = Length of one of the equal sides

Examples

A triangle has a base of 4cm and a height of 6cm, what is the area of the triangle?

We can calculate the area of the triangle using the following formula.

Area=12×Base×Perpendicular Height=12×4  cm×6  cm=12  cm2\begin{aligned} \text{Area} &= \normalsize \dfrac{1}{2} \times \text{Base} \times \text{Perpendicular Height} \\[10pt] &= \dfrac{1}{2} \times 4 \;cm \times 6 \; cm \\[10pt] &= 12 \; cm^2 \end{aligned}

A triangle has 2 sides of 5 cm and one side of 6 cm what is the area of the triangle?

The area of the triangle, for which we know the length of the sides can be calculated by Heron’s formula.

s=a+b+c2=5  cm+5  cm+6  cm2=8  cmA=s(s−a)(s−b)(s−c)=8(8−5)(8−5)(8−6)=144=12  cm2\begin{aligned} s &= \normalsize \dfrac{a + b + c}{2} \\[10pt] &= \normalsize \dfrac{5\;cm + 5\;cm + 6\;cm}{2} \\[10pt] &= 8 \; cm \\[10pt] A &= \sqrt{s(s-a)(s-b)(s-c)} \\[10pt] &=\sqrt{8(8-5)(8-5)(8-6)} \\[10pt] &=\sqrt{144} \\[10pt] &= 12\; cm^2 \end{aligned}
Author

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Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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