Find the area of the parallelogram with vertices A(-3, 0),

Carol Gates

Carol Gates

Answered question

2021-08-17

Find the area of the parallelogram with vertices A(-3, 0), B(-1 , 3), C(5, 2), and D(3, -1).

Answer & Explanation

casincal

casincal

Skilled2021-08-18Added 82 answers

Calculations:
We can choose any three of the supplied points and dind a two vector that expresses the sides of the parallelogram "or one side and a diagonal of the parallelogram," we can choose the points B, C, and D.
Furthermore, we can choose point B as the common point for the two sides "the initial point of the two vectors," so we must find vector BD and vector BC using the equation below.
BC=<5+1,23>
=<6,1>
And, the other vector side BD is
BD=<3+1,13>
=<4,4>
Furthermore, the cross product of both vectors is
BC×BD=<6,1>×<4,4>
=|ijk610440|
=i|1040|j|6040|+k|6144|
=0i0j+k((6)(4)(1)(4))
=20k
Knowing the cross product of the parallelogram's two vectors, we may apply an equation to get the area.
Area=|20k|
=20
As a result, the parallelogram's area is 20 units squared.

xleb123

xleb123

Skilled2023-06-17Added 181 answers

Step 1:
Given:
Area=|12((x2x1)(y4y1)(x4x1)(y2y1))|
Let's calculate the area using the given vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3, -1).
We can label the coordinates as follows:
A(3,0), B(1,3), C(5,2), and D(3,1).
Step 2:
Now, we substitute these values into the formula:
Area=|12((1(3))(20)(3(3))(30))|
Simplifying further:
Area=|12((2)(2)(6)(3))|
Area=|12(418)|
Area=|12(14)|
Taking the absolute value:
Area=12·14
Finally, evaluating the expression:
Area=7
Therefore, the area of the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3, -1) is 7 square units.
Andre BalkonE

Andre BalkonE

Skilled2023-06-17Added 110 answers

Answer: 20
Explanation:
Area=|12((x1x3)(y2y4)(x2x4)(y1y3))|
Substituting the coordinates of the given vertices, we have:
Area=|12(((3)5)(3(1))((1)3)(02))|
Simplifying the expression:
Area=|12((8)(4)(4)(2))|
Area=|12(328)|
Area=|12(40)|
Area=|20|
Area=20
Hence, the area of the parallelogram is 20 square units.
fudzisako

fudzisako

Skilled2023-06-17Added 105 answers

To find the area of the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3, -1), we can use the formula:
Area=|12·(x1y2+x2y3+x3y4+x4y1x2y1x3y2x4y3x1y4)|
where (x1,y1),(x2,y2),(x3,y3),(x4,y4) are the coordinates of the four vertices of the parallelogram.
Substituting the given coordinates into the formula, we have:
Area=|12·((3)(3)+(1)(2)+(5)(1)+(3)(0)(1)(0)(5)(3)(3)(1)(3)(2))|
Simplifying the expression inside the absolute value:
Area=|12·(925+0+015+3+6)|
Area=|12·(22)|
Area=|11|
Therefore, the area of the parallelogram is 11 square units.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?