Comments for Area List

Comment on Why does the matrix area formula for a triangle work? by SCAR

SCAR — Tue, 09 Mar 2010 08:44:59 +0000

It stems from the property that the area of a parallelogram with two vectors as adjacent sides is equal to the determinant of a matrix with those vectors as rows. For instance, suppose you have a parallelogram with one edge <1,1> and the adjacent edge <0,1>. If you form the matrix ‘A’
[ 1 1]
[ 0 1]

and compute the determinant, you get det(A) = 1, which is the area of the parallelogram. If now you only want the area of the triangle with sides <1,1> and <0,1>, you divide by 2. Or 1/2*det(A) = area of triangle.

IF you now draw any triangle with three vertices, and draw vectors from the origin to each vertex, you’ll see that each pair of vectors forms a triangle. Summing the area of these individual triangles (and recognizing that the order of one pair might make "negative area") gives the area enclosed by the three vertices, when divided by 2.

The matrix you show is a simple way to combine the three separate determinants into one.
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Comment on How do I use Heron’s Formula to find the area of the triangle? by Mujtaba Y

Mujtaba Y — Sun, 07 Mar 2010 08:59:59 +0000

find the length of each side
let the consecutive odd numbers be a=x ,b= x+2, c=x+4
formula for a perimeter {a+b+c=105}

x + (x+2) + (x+4) = 105
x+x+x=99
3x=99
x=33

therefore length of each side is
a=33, b=35, c=37

then just plug this into the herrons formula’s

step one:
find half the parimeter (set as variable H impling half perimeter)

step two use:
Find area,
area = squareroot (H (H-a) (H-b) (H-c))

just plug in the numbers and u got the answer…. not doing the calculation cuz the best way to understand math is by doing it urself even if u hate it.
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Comment on What is the area formula for a circle? by kingofclubs_uk

kingofclubs_uk — Fri, 05 Mar 2010 10:12:59 +0000

If you can imagine cutting the circle into really thin sectors – so thin that the curve of the circumference is lost – and you then arrange them one pointing up, one pointing down, one pointing up, one pointing down etc.. You will get a rectangle.

The vertical side of the rectangle will be equal to the radius. The horizontal sides at the top and bottom will total the circumference (2 pi r)

As to find area we multiply horizontal by vertical, we only want the value of one horizontal side. 2 pi r / 2 = pi r.

So area or a circle = pi r x r = pi r^2
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Comment on What is the area formula for a circle? by michaelempeigne

michaelempeigne — Fri, 05 Mar 2010 09:55:59 +0000

A = pi*r^2
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my brain

Comment on What is the area formula for a circle? by MR SCM

MR SCM — Fri, 05 Mar 2010 09:33:59 +0000

π r² where r is the radius.
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Comment on What is the area formula for a circle? by MS. B

MS. B — Fri, 05 Mar 2010 09:12:59 +0000

A= pi* r^2 The area is equal to pi times the radius squared. If you do not have the radius, use the diameter. The radius is equal to the diameter divided by 2.
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Comment on What is the area formula for a circle? by Retsum

Retsum — Fri, 05 Mar 2010 09:07:59 +0000

pi.r^2
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Comment on What is the area formula for a circle? by KC

KC — Fri, 05 Mar 2010 08:23:59 +0000

π r²
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Comment on What is the area formula for a circle? by harry m

harry m — Fri, 05 Mar 2010 07:55:59 +0000

What is the area formula for a circle? = pi * r^2 QED
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Comment on How do you find the area of a triangle using the determinant of a matrix, only working backwards? by Catalina_romania

Catalina_romania — Fri, 05 Mar 2010 07:28:59 +0000

I hope you’ll understand what i’m going` to write (i’m from Romania, in the last year of high school)
First of all, I would note the determinant of the matrix with D and the area with A , to simplify our work.
The formula of the area is : A=1/2 * | D |
the determinant looks like that :
-5 1 1
0 2 1
-2 x 1
now, we’ll solve the determinant with the triangle’s formula =>
D= -10 + 0 -2 + 4 + 5x + 0 = -12 + 4 + 5x = 5x – 8
We know that A = 4 => 1/2 * | D | = 4 => | D | = 8 => 5x – 8 = 8 =>
x = 16/5
hope it will help you in some way
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