Question

question 4 (multiple choice worth 4 points) (04.06r lc) what is the area of trapezoid defg with coordinates d (2, 3), e (4, 3), f (6, 1), and g (2, 1)? 12 square units 8 square units 6 square units 3 square units

Explanation:

Step1: Find lengths of bases and height

The length of base 1 ($b_1$): The distance between $D(2,3)$ and $E(4,3)$ is $|4 - 2|=2$ using the distance formula for points on a horizontal line ($y$-coordinates are the same).
The length of base 2 ($b_2$): The distance between $F(6,1)$ and $G(2,1)$ is $|6 - 2| = 4$ using the distance formula for points on a horizontal line ($y$-coordinates are the same).
The height ($h$): The distance between the two horizontal - lines $y = 3$ and $y = 1$ is $|3 - 1|=2$.

Step2: Apply trapezoid area formula

The area formula of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$. Substitute $b_1 = 2$, $b_2 = 4$, and $h = 2$ into the formula: $A=\frac{(2 + 4)\times2}{2}$.
First, calculate the sum of the bases: $2+4 = 6$. Then, multiply by the height: $6\times2=12$. Finally, divide by 2: $\frac{12}{2}=6$.

Answer:

6 square units