# What is the formula to find area of a triangle using determinants?

## What is the formula to find area of a triangle using determinants?

Area of Triangle Using Determinant

1. k = ½ [ x1 ( y2 – y3 ) + x2 ( y3 – y1 ) + x3 ( y1 – y2 ) ]
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3. In order to find the area of a triangle in determinant form, you use the formula given below:

### How do you find the area of a triangle using vertices?

Given the coordinates of the three vertices of any triangle, the area of the triangle is given by:

1. A. x. ( B. y. − C. y. )
2. B. x. ( C. y. − A. y. )
3. C. x. ( A. y. − B. y. )

How do you find the area using coordinates?

By finding the product of a point’s x coordinate times the next point’s y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon.

When to use matrices to find the area of a triangle?

When the determinant of the matrix used to find area of a triangle is zero the 3 points are collinear. (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively.

## How to find out the area of a triangle using determinants?

Now let us try our hands at this application of determinants to find out the area of triangles. Example: Find out the area of the triangle whose vertices are given by A (0,0) , B (3,1) and C (2,4). Solution: Using determinants we can easily find out the area of the triangle obtained by joining these points using the formula

### How to calculate the area of an acute triangle?

These formulas are very easy to remember and also to calculate. For example, If, in ∆ABC, A = 30° and b = 2, c = 4 in units. Then the area will be; Find the area of an acute triangle with a base of 13 inches and a height of 5 inches. Find the area of a right-angled triangle with a base of 7 cm and a height of 8 cm.

How do you find the area of a scalene triangle?

Answer: A scalene triangle is one which all three sides of different lengths. The area of a scalene triangle that has a base b and height h is given by 1/2 bh. If one knows the lengths of all three sides, one can find area by making use of the Heron’s Formula without the need to find the height.