Triangle Area and Matrix Methods

This video tutorial explains how to calculate the area of a triangle using the vertices of the triangle. It introduces the use of a 3x3 matrix and the determinant to find the area. Two examples are provided to demonstrate the calculation process. The video also covers graphical confirmation of the area and introduces Heron's formula as an alternative method. The tutorial emphasizes the ease of using matrices for such calculations.

What is the formula used to calculate the area of a triangle using a 3x3 matrix?

• 1/3 the absolute value of the determinant

• 1/2 the absolute value of the determinant

• The sum of the matrix elements

• The product of the matrix elements

In the first example, what are the x-coordinates of the vertices used?

• 3, 7, -5

• 2, 5, 10

• 1, 1, 5

• 1, 4, 4

What is the determinant of the matrix for the first example?

• 6

• 8

• 12

• 25

In the second example, what is the y-coordinate of the third vertex?

• 5

• -5

• 7

• 3

What is the area of the triangle in the second example using the matrix method?

• 14 square units

• 12 square units

• 28 square units

• 56 square units

Which theorem is used to verify the side lengths in the graphing method?

• Determinant theorem

• Matrix theorem

• Heron's theorem

• Pythagorean theorem

What is the hypotenuse of the 3-4-5 triangle?

• 3

• 6

• 4

• 5

What is the formula used to calculate the area of a triangle using Heron's formula?

• a * b * c

• a^2 + b^2 = c^2

• s * (s-a) * (s-b) * (s-c)

• 1/2 * base * height

What is the approximate value of s in Heron's formula for the complex example?

• 9

• 12

• 16.65

• 28

Which method is considered easier for calculating the area of a triangle given the vertices?

• Graphing method

• Matrix method

• Heron's formula

• Pythagorean theorem