Question

triangle abc, with vertices a(-9,4), b(-5,3), and c(-4,9), is drawn inside a rectangle, as shown below.
what is the area, in square units, of triangle abc?

Explanation:

Step1: Find rectangle dimensions

Width: $|-4 - (-9)| = 5$, Height: $|9 - 3| = 6$
Area of rectangle: $5 \times 6 = 30$

Step2: Calculate area of Triangle 1

Base=4, Height=1. Area: $\frac{1}{2} \times 4 \times 1 = 2$

Step3: Calculate area of Triangle 2

Base=5, Height=5. Area: $\frac{1}{2} \times 5 \times 5 = 12.5$

Step4: Calculate area of Triangle 3

Base=1, Height=6. Area: $\frac{1}{2} \times 1 \times 6 = 3$

Step5: Subtract areas from rectangle

$30 - (2 + 12.5 + 3) = 30 - 17.5$

Answer:

12.5 square units