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

In this lesson, we will learn how to use determinants to calculate areas of triangles and parallelograms given the coordinates of their vertices.

Lesson Plan

Students will be able to

find the area of a triangle using determinants
- when given a graph of the triangle in the coordinate plane,
- when given the coordinates of the triangle’s vertices,
find the area of a parallelogram using determinants
- when given a graph of the parallelogram in the coordinate plane,
- when given at least 3 coordinates of the parallelogram’s vertices,
determine whether three points are collinear by finding the area of the triangle they construct.

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.

Q3:

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