Answer:
50 units²
Step-by-step explanation:
It's helpful, but not absolutely mandatory, to sketch the rectangle. Doing this clearly positions the length and width of the rectangle.
The length of the line segment connecting A and B is the width of the rectangle, and that connection A and D is the length.
Use the Pythagorean Theorem to find the length and width:
length: Moving from A to D, we see that x increases by 8 units and that y increases by 6 units. Thus, the length of line segment AD is
|AD|² = 6² + 8² = 10², so |AD| = 10.
Similarly, the length of line segment AB is
|AB|² = 3² + 4² = 5², so that |AB| = 5.
The area of the rectangle is thus (length)(width) = (10)(5) = 50 units²
