square with side length √17 units, so area 17 square units.
Step-by-step explanation:
Each side has a slope with a rise of 1 and a run of 4, or a rise of -4 and a run of 1. The ratios of these numbers are opposite reciprocals, so we know the sides are perpendicular. The sum of squares of these numbers is 17, so we know the sides are √17 and all are the same length. (The Pythagorean theorem tells us this.)
A quadrilateral with equal-length perpendicular sides is a square. This square has side length √17 units and area (√17)² = 17 square units.
