Worksheet: Using Determinants to Calculate Areas

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 𝐴𝐡𝐢 with vertices 𝐴(1,4), 𝐡(βˆ’4,5), and 𝐢(βˆ’4,βˆ’5).

Q3:

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

Q4:

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

Q5:

Consider the quadrilateral with vertices 𝐴(1,3),𝐡(4,2),𝐢(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 ||||𝐡𝐢000𝐴𝐢000𝐴𝐡||||=936. If triangle 𝐴𝐡𝐢 is right triangle at 𝐡. It 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 𝐴𝐡𝐢 with vertices 𝐴(1,βˆ’5), 𝐡(βˆ’4,βˆ’2), and 𝐢(5,βˆ’5).

Q15:

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

  • A14
  • B31
  • C312
  • D16
  • E10

Q16:

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

Q17:

Use determinants to calculate the area of the parallelogram with vertices (1,1), (βˆ’4,5), (βˆ’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 (π‘Ž,𝑏),(4+π‘Ž,1+𝑏),(5+π‘Ž,4+𝑏), and (1+π‘Ž,3+𝑏).

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

Q19:

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

Q20:

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

  • A𝐴(βˆ’3,6), 𝐡(8,βˆ’7), 𝐢(βˆ’3,βˆ’8)
  • B𝐴(βˆ’10,βˆ’6), 𝐡(βˆ’2,1), 𝐢(0,βˆ’9)
  • C𝐴(βˆ’6,4), 𝐡(βˆ’8,4), 𝐢(3,10)
  • D𝐴(βˆ’10,βˆ’4), 𝐡(βˆ’8,βˆ’2), 𝐢(βˆ’5,1)

Q21:

The area of a triangle whose vertices are 𝐴(βˆ’2,βˆ’3), 𝐡(4,βˆ’3), and 𝐢(0,8) equals square units.

  • A33
  • B44
  • C66
  • D132

Q22:

If the area of a triangle whose vertices are (β„Ž,0), (6,0), and (0,3) is 9 square units, then β„Ž=.

  • Aβˆ’6 or 6
  • B0 or 12
  • Cβˆ’12 or 12
  • D0 or βˆ’12

Q23:

The area of the triangle whose vertices are 𝐴(2,3), 𝐡(βˆ’1,6), and 𝐢(3,4) equals square units.

  • A6
  • B9
  • C3
  • D12

Q24:

The area of the triangle with vertices (2,3), (0,0), and (8,0) equals square units.

  • A6
  • B24
  • C48
  • D12

Q25:

The area of the triangle whose vertices are (4,3), (6,3), and (6,4) equals square units.

  • A8
  • B2
  • C1
  • D4

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