What is the area of rectangle DEFG?

Question

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.