Area of Triangles and Parallelograms

This video tutorial explains how to use determinants to calculate the area of triangles and parallelograms on a coordinate plane. It covers the formula for the area of a triangle using a 3x3 determinant and demonstrates the calculation process using both the diagonal and cofactor expansion methods. The tutorial also shows how to find the area of a parallelogram by dividing it into two congruent triangles and using the same determinant method. The video concludes with a review of the methods discussed.

What is the formula for the area of a triangle on the coordinate plane using determinants?

• 1/3 x the value of a 3x3 determinant

• + or - 1/3 x the value of a 2x2 determinant

• + or - 1/2 x the value of a 3x3 determinant

• 1/2 x the value of a 2x2 determinant

Why is there a '+ or -' in the formula for the area of a triangle using determinants?

• To account for the possibility of negative coordinates

• To adjust for the order of vertices in the determinant

• To ensure the determinant is always positive

• To simplify the calculation process

In the example of finding the area of a triangle, what is the final area calculated?

• 15 square units

• 20 square units

• 10 square units

• 5 square units

What method is used to evaluate the determinant in the triangle area example?

• Matrix inversion

• Row reduction

• Diagonal method

• Cofactor expansion

How is the area of a parallelogram determined using the triangle area formula?

• By finding the area of one triangle and multiplying by four

• By finding the area of one triangle and multiplying by two

• By using a 4x4 determinant

• By finding the area of two triangles and adding them

What is the first step in calculating the area of a parallelogram using determinants?

• Use a 2x2 determinant for each triangle

• Calculate the perimeter of the parallelogram

• Draw a diagonal to form two triangles

• Label all the coordinates of the vertices

In the parallelogram example, what is the area of one of the triangles?

• 2 square units

• 4 square units

• 6 square units

• 8 square units

Which method is used to evaluate the determinant in the parallelogram example?

• Matrix inversion

• Cofactor expansion

• Diagonal method

• Row reduction

What is the total area of the parallelogram calculated in the example?

• 8 square units

• 16 square units

• 10 square units

• 12 square units

What are the two methods reviewed for evaluating a 3x3 determinant?

• Cofactor expansion and matrix inversion

• Diagonal and row reduction

• Row reduction and matrix inversion

• Diagonal and cofactor expansion