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