# 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.

**Q4: **

Use determinants to work out the area of the triangle with vertices , , and by viewing the triangle as half of a parallelogram.

**Q5: **

Consider the quadrilateral with vertices , and .

By breaking it into two triangles as shown, calculate the area of this quadrilateral using determinants.

**Q6: **

Consider the equation If triangle is right triangle at . It has an area of 39, what is the radius of its circumcircle?

**Q15: **

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

- A14
- B31
- C
- D16
- E10

**Q16: **

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

**Q18: **

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 .

**Q19: **

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

**Q20: **

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 .
- Bis 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

**Q21: **

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

- A, ,
- B, ,
- C, ,
- D, ,