# Lesson Worksheet: Using Determinants to Calculate Areas Mathematics

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 a right triangle at and 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: **

If the area of the triangle with vertices at , , and is 3, use determinants to find the value of .

**Q22: **

Consider a triangle in which , , and are the midpoints of its sides. Use determinants to find the area of triangle .

- A10 square units
- B7.5 square units
- C15 square units
- D5 square units
- E20 square units

**Q23: **

Consider a parallelogram in which , , and are three vertices.

Complete the following: The area of this parallelogram equals square units.

**Q25: **

If the area of the triangle with vertices , , and equals triple the area of the parallelogram in which the points , , and are vertices, find all possible values of .

- A
- B and
- C and 2
- D and
- E2