Question

a polygon has vertices r(1,1), s(1,4), and t(5,1). what is the area of the polygon? a) 4 square units b) 6 square units c) 8 square units d) 12 square units

Explanation:

Step1: Identify polygon type

The 3 vertices form a right triangle.

Step2: Calculate leg lengths

Horizontal leg: $5-1=4$ units
Vertical leg: $4-1=3$ units

Step3: Apply triangle area formula

Area = $\frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area} = \frac{1}{2} \times 4 \times 3$

Step4: Compute final area

$\text{Area} = 6$ square units

Answer:

B) 6 square units