What is the area in square units of △ABC with vertices A(1, 3), B(3, 2) and C(−4, −2)?

Correct answer: a 15/2 square units

½|1(2 + 2) + 3(−2 − 3) + (−4)(3 − 2)| = ½|4 − 15 − 4| = 15/2 square units.

Why the other options are wrong

• b 15 square units: 15 is the value of the determinant; the area is half of it, 15/2.
• c 25/2 square units: ½|1(2 + 2) + 3(−2 − 3) + (−4)(3 − 2)| = ½|4 − 15 − 4| = 15/2 square units. So 25/2 square units is not the answer.
• d 30 square units: ½|1(2 + 2) + 3(−2 − 3) + (−4)(3 − 2)| = ½|4 − 15 − 4| = 15/2 square units. So 30 square units is not the answer.