Question

lets try:
find the area of rectangle efgh. round to the nearest tenth if necessary.
e(-2, 6), f(4, 3), g(2, -1), h(-4, 2)

1. graph quadrilateral efgh.
2. find the length of ef or gh.
3. find the length of eh or fg.
4. multiply the length by the width to find the area of efgh.

Explanation:

Step1: Find length of EF

Use distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ for $E(-2,6)$ and $F(4,3)$.
$EF = \sqrt{(4 - (-2))^2 + (3 - 6)^2} = \sqrt{6^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.7$

Step2: Find length of EH

Use distance formula for $E(-2,6)$ and $H(-4,2)$.
$EH = \sqrt{(-4 - (-2))^2 + (2 - 6)^2} = \sqrt{(-2)^2 + (-4)^2} = \sqrt{4 + 16} = \sqrt{20} \approx 4.5$

Step3: Calculate area of rectangle

Area = length × width = $EF × EH \approx 6.7 × 4.5 = 30.15 \approx 30.2$ (rounded to nearest tenth)

Answer:

The area of rectangle EFGH is approximately 30.2.