# 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.

**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: **

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

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

**Q21: **

The area of a triangle whose vertices are , , and equals square units.

- A33
- B44
- C66
- D132

**Q23: **

The area of the triangle whose vertices are , , and equals square units.

- A6
- B9
- C3
- D12

**Q24: **

The area of the triangle with vertices , , and equals square units.

- A6
- B24
- C48
- D12

**Q25: **

The area of the triangle whose vertices are , , and equals square units.

- A8
- B2
- C1
- D4