# Lesson Worksheet: Using Determinants to Calculate Areas Mathematics • 10th Grade

In this worksheet, we will practice using determinants to calculate areas of triangles and parallelograms given the coordinates of their vertices.

Q1:

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

Q2:

Find the area of the triangle below using determinants. • A18 square units
• B26 square units
• C13 square units
• D36 square units

Q3:

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

Q4:

Using determinants, are the points , , and collinear?

• ANo
• BYes

Q5:

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

Q6:

Fill in the blank: If the area of a triangle whose vertices are , , and is 9 square units, then .

• A or 6
• B0 or
• C0 or 12
• D12 or

Q7:

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

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

Q8:

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

• A, ,
• B, ,
• C, ,
• D, ,

Q9:

If the points , , and are collinear, use determinants to find all the possible values of . Round your answers to two decimal places.

• A1.00 and 3.00
• B1.08 and
• C4.32 and
• D3.00 and
• E2.16 and

Q10:

Given the points , , , and , find the values of and if the area of the triangle is 2 square units and the points , , and are collinear.

• A or and
• B or and
• C or 5 and
• D or 5 and
• E and