Find the area of the quadrilateral whose vertices are A(−4, −3), B(3, −1), C(3, 2) and D(−2, 4).

1. 1 · Write what is given and what is to be found Given: A(−4, −3), B(3, −1), C(3, 2), D(−2, 4). To find: the area of quadrilateral ABCD.
2. 2 · Draw the figure Plot the four points. A is bottom left, B bottom right, C top right and D top left, so A → B → C → D is anticlockwise.
3. 3 · Write the formula Area = (1/2){(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) − (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)}
4. 4 · Find the first sum (−4)(−1) + (3)(2) + (3)(4) + (−2)(−3) = 4 + 6 + 12 + 6 = 28
5. 5 · Find the second sum (3)(−3) + (3)(−1) + (−2)(2) + (−4)(4) = −9 − 3 − 4 − 16 = −32
6. 6 · Subtract and halve (1/2){28 − (−32)} = (1/2)(60) = 30
7. 7 · Check and box the answer Area of ABCD = 30 sq. units.

Scoring tip: Write the four points in two columns and repeat A at the bottom. Then the products are easy to read off without mistakes.