Area of Triangle Formula

We all know that a triangle is a polygon, which has three sides. The area of a triangle is a measurement of the area covered by the triangle. We can express the area of a triangle in the square units. The area of a triangle is determined by two formulas i.e. the base multiplies by the height of a triangle divided by 2 and second is Heron’s formula. Let us discuss the Area of a Triangle formula in detail.

                                                                                                                                                                     Source: Youtube.com

Area of Triangle a Formula

What is an Area of a triangle?

The area of a polygon is the number of square units covered by the polygon. The area of a triangle is determined by multiplying the base of the triangle and the height of the triangle and then divides it by 2. The division by 2 is done because the triangle is a part of a parallelogram that can be divided into 2 triangles.

Area of a parallelogram = B × H

Where,

B	the base of the parallelogram
H	the height of the parallelogram

As triangle is the one-half of the parallelogram, so the area of a triangle is:

A= 12×b×h

Where,

B	the base of the triangle
H	the height of the triangle

Heron’s Formula for Area of a Triangle

Herons formula is a method for calculating the area of a triangle when the lengths of all three sides of the triangle are given.

Let a, b, c are the lengths of the sides of a triangle.

The area of the triangle is:

Area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

Where, s is half the perimeter,

s= a+b+c2

We can also determine the area of a triangle by the following methods:

1. In this method two Sides, one included Angle is given

Area= 12×a×b×sinc

Where a, b, c are the lengths of the sides of a triangle

2. In this method we find area of an Equilateral Triangle

Area= 3√×a24

3. In this method we find area of a triangle on a coordinate plane by Matrices

12×⎡⎣⎢x1x2x3y1y2y3111⎤⎦⎥

Where, (x1, y1), (x2, y2), (x3, y3) are the coordinates of the three vertices

4. In this method, we find area of a triangle in which two vectors from one vertex is there.

Area of triangle = 12(u→×v→)

Solved Examples

Q.1: The sides of a right triangle ABC are 5 cm, 12 cm, and 13 cm.

Solution: In △ABC in which base= 12 cm and height= 5 cm

Area of △ABC=12×B×H

A = 12×12×5

A = 30 cm2

Q.2: Find the area of a triangle, which has two sides 12 cm and 11 cm and the perimeter is 36 cm.

 Solution: Here we have perimeter of the triangle = 36 cm, a = 12 cm and b = 11 cm.

Third side c = 36 cm – (12 + 11) cm = 13 cm

So, 2s = 36, i.e., s = 18 cm,

s – a = (18 – 12) cm = 6 cm,

s – b = (18 – 11) cm = 7 cm,

and, s – c = (18 – 13) cm = 5 cm.

Area of the triangle = s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

A= 18×6×7×5−−−−−−−−−−−√

A= 6105−−−√ cm2