the formula 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 51 square units 52 square units 53 square units

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $AB$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $A(-1,6)$ and $B(4,5)$, $x_1=-1,y_1 = 6,x_2=4,y_2 = 5$.
$$
\begin{align*}
AB&=\sqrt{(4-(-1))^2+(5 - 6)^2}\
&=\sqrt{(4 + 1)^2+(-1)^2}\
&=\sqrt{25+1}\
&=\sqrt{26}
\end{align*}
$$
## Step2: Calculate the length of $BC$
For $B(4,5)$ and $C(2,-5)$, $x_1 = 4,y_1=5,x_2=2,y_2=-5$
$$
\begin{align*}
BC&=\sqrt{(2 - 4)^2+(-5 - 5)^2}\
&=\sqrt{(-2)^2+(-10)^2}\
&=\sqrt{4 + 100}\
&=\sqrt{104}=2\sqrt{26}
\end{align*}
$$
## Step3: Calculate the area of rectangle $ABCD$
Since $A=lw$ (for rectangle $ABCD$, $l = BC$, $w=AB$)
$$
\begin{align*}
A&=AB\times BC\
&=\sqrt{26}\times2\sqrt{26}\
&=2\times26\
&=52
\end{align*}
$$

# Answer:
52 square units

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Question

Explanation:

Step1: Calculate the length of \(AB\)

Step2: Calculate the length of \(BC\)

Step3: Calculate the area of rectangle \(ABCD\)

Answer: