Question

What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3) ? Enter your answer in the box. units²

Answer 1

The area of the parallelogram is $\boxed{\bf 90\text{\bf square units}}$.

Further explanation:

Given:

The vertices of a parallelogram are $\text{A}(-12,2)$, $\text{B}(6,2)$, $\text{C}(-2,-3)$, and $\text{D}(-20,-3)$ as shown in attached Figure 1.

Calculation:

As we know that a parallelogram is a quadrilateral having opposite sides parallel and equal in length such that $\text{AB}=\text{CD}$ and $\text{AD}=\text{BC}$.

So the area of a parallelogram is calculated as follows:

$\boxed{\text{A}=\text{b}\cdot \text{h}}$

Where $\text{b}$ is the base and $\text{h}$ is the height.

Draw perpendicular from $\text{A}$ on $\text{CD}$ which meets at point $\text{E}$ as shown in attached Figure 2.

So we have to find the distance $\text{AB}$ and $\text{AD}$ by the formula as shown below:

$\boxed{d=\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}}$

 

Where, $d$ is the distance between the points and $(x_{1},y_{1})$ and $(x_{2},y_{2})$.

The point of $\text{A}$ and $\text{B}$ are $(-12, 2)$ and $(6, 2)$ respectively and distance $\text{AB}$ is calculated as, shown below:

$\begin{aligned}\text{AB}&=\sqrt{(2-2)^{2}+(6-(-12))^{2}}\\&=\sqrt{0^{2}+18^{2}}\\&=\sqrt{18^{2}}\\&=18\end{aligned}$

The coordinates of $A$ and $E$ are $(-12,2)$ and $(-12,-3)$ respectively and distance $\text{AE}$ is calculated as shown below:

$\begin{aligned}\text{AE}&=\sqrt{(-3-2)^{2}+(-12-(-12))^{2}}\\&=\sqrt{(-5)^{2}+0^{2}}\\&=5\end{aligned}$

 

Since, $\text{AB}=\text{CD}$ which is $18$ units and $\text{CD}$ is the base and $\text{AE}$ is the height which is $5$ units as shown in attached figure 2.

Then the area of parallelogram is calculated as shown below:

$\begin{aligned}\text{Area}&=\text{Base}\cdot \text{Height}\\&=\text{CD}\cdot \text{AE}\\&=18\cdot 5\\&=90\end{aligned}$

 

Therefore, area of the parallelogram is $\boxed{\bf 90\text{\bf square units}}$.

Learn more:

1. Learn more about the quantity in meters expressed in centimeters brainly.com/question/2867118

2. Learn more about the 3 digits in the units period brainly.com/question/558692

3. Learn more about the definition of an angle uses the undefined term brainly.com/question/3413207

Answer detail:

Grade: Middle school

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: parallelogram, A(−12,2), B(6,2), C(−2,−3), and D(−20,−3), 90 square units, area, height, base, Coordinate geometry, vertices, perpendicular.

Answer 2

Let

$A(-12,2)\\B(6,2)\\C(-2,-3) \\D(-20.-3)\\E(-12.-3)$

using a graphing tool

see the attached figure to better understand the problem

we know that

Parallelogram is a quadrilateral with opposite sides parallel and equal in length

so

$AB=CD \\AD=BC$

The area of a parallelogram is equal to

$A=B*h$

where

B is the base

h is the height

the base B is equal to the distance AB

the height h is equal to the distance AE

Step 1

Find the distance AB

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(-12,2)\\B(6,2)$

substitute the values

$d=\sqrt{(2-2)^{2}+(6+12)^{2}}$

$d=\sqrt{(0)^{2}+(18)^{2}}$

$dAB=18\ units$

Step 2

Find the distance AE

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(-12,2)\\E(-12.-3)$

substitute the values

$d=\sqrt{(-3-2)^{2}+(-12+12)^{2}}$

$d=\sqrt{(-5)^{2}+(0)^{2}}$

$dAE=5\ units$

Step 3

Find the area of the parallelogram

The area of a parallelogram is equal to

$A=B*h$

$A=AB*AE$

substitute the values

$A=18*5=90\ units^{2}$

therefore

the answer is

the area of the parallelogram is $90\ units^{2}$