Lesson Worksheet: Using Determinants to Calculate Areas Mathematics

In this worksheet, we will practice using determinants to calculate areas of triangles and parallelograms given the coordinates of their vertices.

Q1:

Find the area of the triangle below using determinants.

  • A18 square units
  • B26 square units
  • C13 square units
  • D36 square units

Q2:

Find the area of the triangle 𝐴𝐵𝐶 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 ||||𝐵𝐶000𝐴𝐶000𝐴𝐵||||=936. If triangle 𝐴𝐵𝐶 is a right triangle at 𝐵 and has an area of 39, what is the radius of its circumcircle?

Q7:

Find the area of the triangle below using determinants.

  • A19 square units
  • B34 square units
  • C17 square units
  • D38 square units

Q8:

Find the area of the triangle below using determinants.

  • A16 square units
  • B44 square units
  • C22 square units
  • D32 square units

Q9:

Find the area of the triangle below using determinants.

  • A15 square units
  • B26 square units
  • C13 square units
  • D30 square units

Q10:

Find the area of the triangle below using determinants.

  • A20 square units
  • B60 square units
  • C30 square units
  • D40 square units

Q11:

Find the area of the triangle below using determinants.

  • A18 square units
  • B6 square units
  • C3 square units
  • D36 square units

Q12:

Find the area of the triangle below using determinants.

  • A11 square units
  • B16 square units
  • C8 square units
  • D22 square units

Q13:

Find the area of the triangle below using determinants.

  • A17 square units
  • B20 square units
  • C10 square units
  • D34 square units

Q14:

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

Q15:

Use determinants to calculate the area of the quadrilateral with vertices (1,1), (3,2), (4,1), and (0,3).

  • A14
  • B31
  • C312
  • D16
  • E10

Q16:

Use determinants to calculate the area of the polygon with vertices (1,1), (1,2), (3,1), (0,3), and (2,1).

Q17:

Use determinants to calculate the area of the parallelogram with vertices (1,1), (4,5), (2,8), and (3,4).

Q18:

Use determinants to calculate the area of the parallelogram with vertices (0,0),(4,1),(5,4), and (1,3).

Use determinants to calculate the area of the parallelogram with vertices (𝑎,𝑏),(4+𝑎,1+𝑏),(5+𝑎,4+𝑏), and (1+𝑎,3+𝑏).

Use determinants to calculate the area of the parallelogram with vertices (3,2),(1,1),(2,2), and (2,1).

Q19:

Use determinants to calculate the area of the polygon with vertices (0,0), (2,1), (4,2), (1,4), and (1,2).

Q20:

By using determinants, determine which of the following sets of points are collinear.

  • A𝐴(3,6), 𝐵(8,7), 𝐶(3,8)
  • B𝐴(10,6), 𝐵(2,1), 𝐶(0,9)
  • C𝐴(6,4), 𝐵(8,4), 𝐶(3,10)
  • D𝐴(10,4), 𝐵(8,2), 𝐶(5,1)

Q21:

If the area of the triangle with vertices at (𝑥,3), (𝑦,0), and (𝑧,3) is 3, use determinants to find the value of |𝑧𝑥|.

Q22:

Consider a triangle 𝐴𝐵𝐶 in which 𝑀(6,3), 𝑁(4,2), and 𝐿(5,0) are the midpoints of its sides. Use determinants to find the area of triangle 𝐴𝐵𝐶.

  • A10 square units
  • B7.5 square units
  • C15 square units
  • D5 square units
  • E20 square units

Q23:

Consider a parallelogram in which (1,3), (3,0), and (1,2) are three vertices.

Complete the following: The area of this parallelogram equals square units.

Q24:

Using determinants, are the points (0,1), 2,12, and (4,0) collinear?

  • ANo
  • BYes

Q25:

If the area of the triangle with vertices (1,), (0,3), and (4,5) equals triple the area of the parallelogram in which the points (1,2), (,0), and (3,4) are vertices, find all possible values of .

  • A2
  • B5 and 0.8
  • C2 and 2
  • D2 and 0.5
  • E2

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.