Question

What is the area of rectangle DEFG?
E = (0,0)
F = (0,3)
G = (9,3)
D = (9,0)
Area = _____ Square Units

Answer 1

To find the area of rectangle DEFG, we first need to determine the lengths of its sides.

The coordinates of each vertex are as follows:
- E = (0, 0)
- F = (0, 3)
- G = (9, 3)
- D = (9, 0)

1. **Length of side EF (height)**:
- EF is a vertical line segment between points E and F.
- The length of EF can be calculated as the difference in the y-coordinates of F and E:
\[
\text{Length of EF} = y_F - y_E = 3 - 0 = 3 \text{ units}
\]

2. **Length of side ED (width)**:
- ED is a horizontal line segment between points E and D.
- The length of ED can be calculated as the difference in the x-coordinates of D and E:
\[
\text{Length of ED} = x_D - x_E = 9 - 0 = 9 \text{ units}
\]

3. **Area of rectangle DEFG**:
- The area (A) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]
- Thus, substituting the lengths we calculated:
\[
A = \text{Length of EF} \times \text{Length of ED} = 3 \times 9 = 27 \text{ square units}
\]

Therefore, the area of rectangle DEFG is \( \boxed{27} \) square units.