Question

ula for the area of a rectangle is a = lw. what is the area of rectangle abcd? round the answer to the nearest whole, if necessary. 50 square units 53 square units 52 square units 51 square units

Explanation:

Step1: Find length of AB

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For A(-1,6) and B(4,5):
$d_{AB} = \sqrt{(4 - (-1))^2 + (5 - 6)^2} = \sqrt{5^2 + (-1)^2} = \sqrt{25 + 1} = \sqrt{26}$

Step2: Find length of BC

For B(4,5) and C(2,-5):
$d_{BC} = \sqrt{(2 - 4)^2 + (-5 - 5)^2} = \sqrt{(-2)^2 + (-10)^2} = \sqrt{4 + 100} = \sqrt{104}$

Step3: Calculate area of rectangle

Area $A = d_{AB} \times d_{BC} = \sqrt{26} \times \sqrt{104} = \sqrt{26 \times 104} = \sqrt{2704} = 52$ (since $26\times104 = 26\times(100 + 4)=2600+104 = 2704$ and $\sqrt{2704}=52$)

Answer:

52 square units