Question

The area of a triangle with vertices A, B, C is given by ______. 

Options

• `|vec("AB") xx vec("AC")|`

• `1/2|vec("AB") xx vec("AC")|`

• `1/4|vec("AC") xx vec("AB")|`

• `1/8|vec("AC") xx vec("AB")|`

Answer 1

The area of a triangle with vertices A, B, C is given by `underline(bb(1/2|vec(AB) xx vec(AC)|))`.

Explanation:

The area of the parallelogram with adjacent sides AB and AC = `|vec("AB") xx vec("AC")|`.  Hence, the area of the triangle with vertices A, B, C = `1/2|vec("AB") xx vec("AC")|`