Lesson: Determinants and Areas of Triangles

In this lesson, we will learn how to calculate areas of triangles using determinants.

Sample Question Videos

  • 03:03
  • 04:10

Worksheet: Determinants and Areas of Triangles • 14 Questions • 2 Videos

Q1:

Find the area of the triangle below using determinants.

Q2:

Find the area of the triangle 𝐴 𝐵 𝐶 with vertices 𝐴 ( 1 , 4 ) , 𝐵 ( − 4 , 5 ) , and 𝐶 ( − 4 , − 5 ) .

Q3:

Use determinants to find the area of the triangle with vertices ( 0 , − 1 ) , ( 0 , 2 ) , and ( 5 , 0 ) .

Q4:

Use determinants to work out the area of the triangle with vertices ( 2 , − 2 ) , ( 4 , − 2 ) , and ( 0 , 2 ) by viewing the triangle as half of a parallelogram.

Q5:

Consider the quadrilateral with vertices 𝐴 ( 1 , 3 ) , 𝐵 ( 4 , 2 ) , 𝐶 ( 4 . 5 , 5 ) , and 𝐷 ( 2 , 6 ) .

By breaking it into two triangles as shown, calculate the area of this quadrilateral using determinants.

Q6:

Consider the equation If triangle 𝐴 𝐵 𝐶 has an area of 38, what is the radius of its circumcircle?

Q7:

Find the area of the triangle below using determinants.

Q8:

Find the area of the triangle below using determinants.

Q9:

Find the area of the triangle below using determinants.

Q10:

Find the area of the triangle below using determinants.

Q11:

Find the area of the triangle below using determinants.

Q12:

Find the area of the triangle below using determinants.

Q13:

Find the area of the triangle below using determinants.

Q14:

Find the area of the triangle 𝐴 𝐵 𝐶 with vertices 𝐴 ( 1 , − 5 ) , 𝐵 ( − 4 , − 2 ) , and 𝐶 ( 5 , − 5 ) .
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