Rectangle 𝐴𝐵𝐶𝐷 is graphed in the coordinate plane with its vertices at 𝐴: zero, zero; 𝐵: six, zero; 𝐶: six, five; and 𝐷: zero, five. Find its area.
We’re told in the question that these four vertices form a rectangle 𝐴𝐵𝐶𝐷. We’re given the coordinates or ordered pairs of each of these vertices. So let’s take some grid paper and see if we can draw grid with these four vertices on it. So here we have a vertex 𝐴 at zero, zero; 𝐵 at six, zero; 𝐶 at six, five; and 𝐷 at zero, five. We can see when we join these four vertices that we do indeed have a rectangle, since each of the angles in this quadrilateral would be of 90 degrees. In order to find the area of this rectangle, we’ll need to recall an important formula. And that is that the area of a rectangle is equal to the length multiplied by the width.
In order to find the value of the length and the width, we’ll need to look a little bit closer at this coordinate grid. Let’s begin with the line that goes between 𝐴 and 𝐵. The length of this would be six units long. We can see that either by counting the squares or by understanding that 𝐵 is at six on the 𝑥-axis and 𝐴 is at zero. Therefore, it must be six units long. In order to find the width or the other dimension, we could look at the line 𝐴𝐷. 𝐷 is at the point five on the 𝑦-axis and 𝐴 is at zero. And so this line would be five units long. In order to find the area then, we take our length and our width of six and five and multiply it together, giving us a value of 30. As area is always given in square units, then we can say that the area of 𝐴𝐵𝐶𝐷 is 30 square units.