Area of triangle using determinants

Last updated at August 2, 2026 by

In a 2D plane,

For three points

   A (x 1 , y 1 ),

  B (x 2 , y 2 ),

  C (x 3 , y 3 )

9.jpg

Find area of triangle with vertices (3, 8), (-4, 2), (5, 1)

Check solution - Example 17

Important Points

There are some points to note:-

  1. If Area of triangle = 0 ,
    then the three points are collinear

  2. If the value of determinant comes negative, we will take the
    positive value as area

    Example
    Area of triangle using determinants - Part 2



    Therefore,
    Area = 45 square units

  3. If area is given,
    We take both positive and negative value of determinant
    Example
    If Area = 3 square units

Area of triangle using determinants - Part 3

 

Check the questions below to learn more

 

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 3 questions, selected from your answers, mistakes, and progress.
Remove Ads

Transcript

Area of ∆ = 1/2 |■8(𝑥_1&𝑦_1&1@𝑥_2&𝑦_2&1@𝑥_3&𝑦_3&1)| For points in 3D plane A (x1, y1, z1) B (x2, y2 , z2) C (x3, y3 , z3) Area of ∆ABC = 1/2 |■8(𝑥_1&𝑦_1&𝑧_1@𝑥_2&𝑦_2&𝑧_2@𝑥_3&𝑦_3&𝑧_3 )| Example If Area = 1/2 |■8(9&2&1@5&−1&6@4&0&−2)| = 1/2 × −90 = −45 Therefore, Area = 45 square units 1/2 |■8(1&3&1@0&0&1@𝑘&0&1)| = ± 3

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.