Use the image to answer the question.

Question

A coordinate plane shows the x-axis ranging from negative 9 to 9 in unit increments and the y-axis ranging from negative 11 to 11 in unit increments. Four plotted points upper A upper B upper C upper D are joined to form a rectangle. The coordinates of the plotted points are as follows: point upper A is left parenthesis 3 comma 4 right parenthesis, point upper B is left parenthesis negative 5 comma 4 right parenthesis, point upper C is left parenthesis negative 5 comma 8 right parenthesis, and point upper D is left parenthesis 3 comma 8 right parenthesis.

Find the area of rectangle ABCD in square feet.

Answer 1

To find the area of rectangle ABCD, we need to determine the lengths of its sides. Using the coordinates of the vertices, we can find these lengths.

**Coordinates of the vertices:**
- Point $A=(3,4)$
- Point $B=(-5,4)$
- Point $C=(-5,8)$
- Point $D=(3,8)$

First, identify the length of one pair of opposite sides (horizontal sides, AB and CD):
- The length from $A$ to $B$: $|3-(-5)|=|3+5|=8$

Next, identify the length of the other pair of opposite sides (vertical sides, AD and BC):
- The length from $A$ to $D$: $|4-8|=|4-8|=4$

Now, calculate the area of the rectangle using the formula for the area of a rectangle:
$$\text{Area}=\text{length}\times \text{width}=8\times 4=32$$

Therefore, the area of rectangle $ABCD$ is $32$ square units.