Table of Contents
What is the formula to find area of a triangle using determinants?
Area of Triangle Using Determinant
- k = ½ [ x1 ( y2 – y3 ) + x2 ( y3 – y1 ) + x3 ( y1 – y2 ) ]
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- 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:
- A. x. ( B. y. − C. y. )
- B. x. ( C. y. − A. y. )
- 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.