Area of Triangle Formula, Area of Isosceles, Equilateral, Right Angled Triangle, Heron's formula, SAS

Table of Contents

The “Area of Triangle” is a basic topic of geometry. The region enclosed by the three sides of any triangle is defined as the area of a triangle. In general, it is equal to half of the base times the height, i.e. A = 1/2 (bxh). As a result, to calculate the area of a triangular polygon, we must first find the base (b) and height (h). Area of Triangle applies to all forms of triangles, including scalene, isosceles, and equilateral triangles. Read the full article to learn how to get the area of a triangle.

Area of Triangle

In the Area of Triangle, it is observed that the triangle’s base and height are perpendicular to each other. The area unit is measured in square units (m2, cm2). In this article, we have discussed the area of the triangle and methods to calculate the area of a triangle. Stay tuned and read the entire article to learn how to calculate the area of a triangle and bookmark this page to get the latest updates of all the articles.

Area of Triangle Formula

There are many ways to calculate the Area of Triangle formula. For example, When we know two sides and the angle between them, we can use trigonometric functions to calculate the area of a triangle. The other method we can apply when we know the lengths of all three sides of a triangle, we can apply Heron’s formula to compute the area of a triangle. Furthermore, the basic formula for calculating the area of a triangle is:

Area of Triangle = A = ½ (b × h) square units

Here A = Area of Triangle

B = Base of Triangle

H = Height of a Triangle

Area of Triangle Formula Image

Area of Triangle in Co-ordinate Geometry

Here we have given the methods to calculate the Area of the Triangle using formulas. The formulas to calculate the area of different types of triangles like an isosceles triangle, equilateral triangle, and right-angled triangle are given below.

Area of an Isosceles Triangle

Two of the sides of an isosceles triangle are equal, and the angles opposite the equal sides are likewise equal.

Area of an Isosceles Triangle = 1/4 b√(4a2 – b2)

Where, b = Base of a Triangle

a = Measure of one of the sides from two equal sides

Area of Right Angled Triangle

A right-angled triangle, often known as a right triangle, has one 90° angle and two 60° angles that add up to 90°. As a result, the height of the triangle is equal to the length of the perpendicular side.

Area of Right Angled Triangle = A = 1/2 × Base × Height

Here A = Area of Triangle

B = Base of Triangle

H = Height of a Triangle

Area of an Equilateral Triangle (without Height)

An equilateral triangle is one with all of its sides equal. The perpendicular traced from the triangle’s vertex to its base divides the base into two equal pieces. To compute the area of an equilateral triangle, we must first determine the length of its sides.

Area of an Equilateral Triangle = A = (√3)/4 × side2

Here, A = Area of Triangle

Side = side of the triangle

Area of Triangle using Heron’s formula

We can use Heron’s formula to calculate the area of a triangle if the lengths of its three sides are given. we must first determine the triangle’s perimeter, which is the distance covered by all three sides and is computed by combining their lengths.

Heron’s formula includes a few crucial steps.

Calculate the semi-perimeter (half perimeter) of the specified triangle by adding all three sides and dividing by two.
Enter the value of the triangle’s semi-perimeter into the primary formula, ‘Heron’s Formula’.
Consider the triangle ABC, which has side lengths a, b, and c. To calculate the triangle’s area, we utilize Heron’s formula – Area = √s(s−a)(s−b)(s−c)
The perimeter of the given triangle is (a + b + c). Therefore,’s’ is the semi-perimeter, which is (a + b + c)/2.

Area of Triangle Formula Table

Below we have given the Area of Triangle formulas to calculate the area of a triangle. Check out the table below:

Particulars	Area of Triangle Formula
When a triangle’s base and height are known.	A = 1/2 (base × height)
When all the sides of a triangle are given like a, b, and c.	Heron’s formula Area of a scalene triangle = √s(s−a)(s−b)(s−c) s = (a + b + c)/2 Where, a, b, and c = sides S = semi-perimeter of triangle
When an angle and two sides of a triangle are given	A = 1/2 × side 1 × side 2 × sin(θ) Where, θ = Angle between the given two sides
When the height and base of the triangle are given.	Area of a right-angled triangle = 1/2 × Base × Height
In the case of an equilateral triangle	Area of an equilateral triangle = (√3)/4 × side2
In the case of an isosceles triangle	Area of an isosceles triangle = 1/4 b√(4a2 – b2) Where, b = base of the triangle the length of an equal side.

Area of a Triangle with Two Sides and the Included Angle (SAS)

Now, in case you are given the two sides of a triangle and the angle between them, how can we calculate its area?
Solution – Consider the triangle ABC, with vertex angles ∠A, ∠B, and ∠C, and sides a, b, and c (image).
If any two sides and the angle between them are supplied, then the formulas to determine the area of a triangle are as follows: