Question

what is the area of rectangle abcd?
43 units²
52 units²
104 units²
208 units²

Explanation:

Step1: Find length of AB

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For A(-5,2) and B(1,6):
$AB = \sqrt{(1 - (-5))^2 + (6 - 2)^2} = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52} = 2\sqrt{13}$

Step2: Find length of BC

For B(1,6) and C(9,-6):
$BC = \sqrt{(9 - 1)^2 + (-6 - 6)^2} = \sqrt{8^2 + (-12)^2} = \sqrt{64 + 144} = \sqrt{208} = 4\sqrt{13}$

Step3: Calculate area of rectangle

Area of rectangle = length × width = $AB × BC = 2\sqrt{13} × 4\sqrt{13} = 8 × 13 = 104$

Answer:

104 units²