Worksheet: Determinants and Area of Parallelograms

In this worksheet, we will practice calculating areas of parallelograms using determinants.

Q1:

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

Q2:

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 ) .

Q3:

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

  • A31
  • B10
  • C16
  • D 3 1 2
  • E14

Q4:

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

Q5:

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

Q6:

The unit square is defined as the square with vertices , , , and . Consider the parallelogram with vertices , , , and .

Explain how the parallelogram can be produced from matrix .

  • A is the image of the unit square after multiplication by .
  • B is the image of the unit square after multiplication by .
  • C is the image of the unit square after multiplication by .

Write the area of as a determinant and determine its value.

  • Aarea
  • Barea
  • Carea
  • Darea
  • Earea

Explain how the parallelogram can be produced from matrix .

  • A is the image of the unit square after multiplication by .
  • B is the image of the unit square after multiplication by .
  • C is the image of the unit square after multiplication by .

Write the area of in terms of the matrix .

  • Aarea
  • Barea
  • Carea
  • Darea
  • Earea

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