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what is the area of rhombus abcd?
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Accepted Answer

# Explanation:
## Step1: Find the length of diagonal $AC$
The formula for the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(-1,4)$ and $C(-1,0)$, $x_1=-1,y_1 = 4,x_2=-1,y_2 = 0$.
$$
\begin{align*}
AC&=\sqrt{(-1-(-1))^2+(0 - 4)^2}\
&=\sqrt{0+(-4)^2}\
&=\sqrt{16}\
&=4
\end{align*}
$$
## Step2: Find the length of diagonal $BD$
For points $B(3,2)$ and $D(-5,2)$, $x_1=-5,y_1 = 2,x_2=3,y_2 = 2$.
$$
\begin{align*}
BD&=\sqrt{(3-(-5))^2+(2 - 2)^2}\
&=\sqrt{(3 + 5)^2+0}\
&=\sqrt{64}\
&=8
\end{align*}
$$
## Step3: Calculate the area of the rhombus
The area formula of a rhombus is $A=\frac{1}{2}d_1d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. Here $d_1 = AC = 4$ and $d_2=BD = 8$.
$$
\begin{align*}
A&=\frac{1}{2}\times4\times8\
&=16
\end{align*}
$$
# Answer:
$16$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the length of diagonal \(AC\)

Step2: Find the length of diagonal \(BD\)

Step3: Calculate the area of the rhombus

Answer: