Question

What is the area of trapezoid DEFG with coordinates D (2, 3), E (5, 3), F (3, 1), and G (2, 1)?

2 square units
3 square units
4 square units
8 square units

Answer 1

To find the area of trapezoid DEFG with the given coordinates \( D(2, 3) \), \( E(5, 3) \), \( F(3, 1) \), and \( G(2, 1) \):

1. **Identify the vertices**:
- D and E form one pair of vertices on the top side (with the same y-coordinate), while F and G form the bottom side.

2. **Identify the lengths of the bases**:
- The length of base DE (top) can be calculated as the difference in x-coordinates of \( E \) and \( D \):
\[
\text{Length of DE} = x_E - x_D = 5 - 2 = 3
\]
- The length of base FG (bottom) can be calculated as the difference in x-coordinates of \( G \) and \( F \):
\[
\text{Length of FG} = x_F - x_G = 3 - 2 = 1
\]

3. **Identify the height of the trapezoid**:
- The height can be calculated as the difference in the y-coordinates between the two bases (y-coordinates of DE and FG):
\[
\text{Height} = y_D - y_F = 3 - 1 = 2
\]

4. **Use the trapezoid area formula**:
The area \( A \) of a trapezoid can be calculated using the formula:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.

Plugging in our values:
\[
A = \frac{1}{2} \times (3 + 1) \times 2
\]
\[
A = \frac{1}{2} \times 4 \times 2
\]
\[
A = \frac{1}{2} \times 8 = 4
\]

5. **Conclusion**:
The area of trapezoid DEFG is \( \boxed{4} \) square units.