Area of Triangle Shaded Region

In summary, the determinant area formula can be used to find the area of a triangle if the given points are known.
  • #1
mathland
33
0
Hello everyone. I am having trouble finding the area of the shaded region using the determinant area formula. I know where to plug in the numbers into the formula. My problem here is finding the needed points in the form (x, y) from the given picture for question 21.

Screenshot_20210115-185039_Drive.jpg
 
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  • #2
Please only post one question per thread.

For the second problem what graphing utilities do have access to? (Assuming they don't want you to find one on the internet.)

-Dan
 
  • #3
problem 21

let point B = (0,0)
A = (-10,25)
C = (18,5)

area of the triangle is half the area of the parallelogram formed by adjacent sides BC and BA which may be found using the cross product of two vectors ...

area = $\dfrac{1}{2}(\vec{BC} \times \vec{BA}) =
\dfrac{1}{2}\begin{vmatrix}
\vec{i} &\vec{j} & \vec{k}\\
18 & 5 & 0\\
-10 & 25 & 0
\end{vmatrix}=
\dfrac{1}{2}\begin{vmatrix}
18 & 5\\
-10 &25
\end{vmatrix}$
 
Last edited by a moderator:
  • #4
topsquark said:
Please only post one question per thread.

For the second problem what graphing utilities do have access to? (Assuming they don't want you to find one on the internet.)

-Dan

I don't need help with 22. I just need the set up for 21.
 
  • #5
skeeter said:
problem 21

let point B = (0,0)
A = (-10,25)
C = (18,5)

area of the triangle is half the area of the parallelogram formed by adjacent sides BC and BA which may be found using the cross product of two vectors ...

area = $\dfrac{1}{2}(\vec{BC} \times \vec{BA}) =
\dfrac{1}{2}\begin{vmatrix}
\vec{i} &\vec{j} & \vec{k}\\
18 & 5 & 0\\
-10 & 25 & 0
\end{vmatrix}=
\dfrac{1}{2}\begin{vmatrix}
18 & 5\\
-10 &25
\end{vmatrix}$

Can you tell me how you came up with the elements of the determinant?
 
  • #6
Beer soaked ramblings follow.
mathland said:
Hello everyone. I am having trouble finding the area of the shaded region using the determinant area formula. I know where to plug in the numbers into the formula. My problem here is finding the needed points in the form (x, y) from the given picture for question 21.

View attachment 10940
Duplicate post from MHF by gufeliz (aka https://mathhelpboards.com/members/harpazo.8631/) that was deleted and who was subsequently banned by topsquark.

You really ought to read your book's relevant section before diving into the exercises.
And you should do it when you're fesh and full of energy; preferably after you've rested and slept (and presumably had some nourishment with coffee shortly afterwards) so that you can maximize your mental energy into understanding and applying what you've been reading and not when "my brain is tired and I am physically exhausted" as you like to embellish it. Regardless of how passionate you are about math, you can't work/study and concentrate as hard at the end of a study session (in your case, the end of a working day) as at the beginning.

mathland said:
I don't need help with 22. I just need the set up for 21.
Fourteen years of Precalculus review should have given you some insight on how to set up your problems on your own. How can you ever hope to fish on your own if you keep asking others to throw the net for you so you can just pull it up without knowing what made others throw the net the way they did.

Alternatively,

Vertices: (0, 25), (10, 0), (28, 5)

Area = $
\dfrac{1}{2}\begin{vmatrix}
\ 0& 25&1\\
10 & 0 & 1\\
28 & 5 & 1
\end{vmatrix}$
https://www.physicsforums.com/attachments/311846._xfImport
The area should be clear to you from this diagram.
If it's not then you really have a big problem.
 
Last edited:

Related to Area of Triangle Shaded Region

What is the formula for finding the area of a triangle?

The formula for finding the area of a triangle is A = 1/2 * b * h, where A represents the area, b represents the base, and h represents the height of the triangle.

How do I find the area of a shaded region in a triangle?

To find the area of a shaded region in a triangle, you first need to find the area of the entire triangle using the formula A = 1/2 * b * h. Then, you can subtract the area of any non-shaded regions from the total area to find the area of the shaded region.

Can the area of a shaded region be negative?

No, the area of a shaded region cannot be negative. The area of a triangle is always a positive value, so even if the shaded region is smaller than the non-shaded region, the area will still be a positive value.

Do I need to know the measurements of all sides of the triangle to find the area of a shaded region?

No, you do not need to know the measurements of all sides of the triangle to find the area of a shaded region. As long as you know the base and height of the triangle, you can use the formula A = 1/2 * b * h to find the area.

Can I use the same formula to find the area of any triangle?

Yes, the formula A = 1/2 * b * h can be used to find the area of any triangle, regardless of its shape or size. This formula is a universal method for finding the area of a triangle.

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