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