# 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 , and .

Q2:

Use determinants to calculate the area of the parallelogram with vertices , and .

Use determinants to calculate the area of the parallelogram with vertices , and .

Use determinants to calculate the area of the parallelogram with vertices , and .

Q3:

Use determinants to calculate the area of the quadrilateral with vertices , , , and .

• A31
• B10
• C16
• D
• E14

Q4:

Use determinants to calculate the area of the polygon with vertices , , , , and .

Q5:

Use determinants to calculate the area of the polygon with vertices , , , , and .

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