Area List » triangle area http://www.thearealist.com Mon, 12 Jul 2010 11:15:05 +0000 http://wordpress.org/?v=2.8.4 en hourly 1 Really need a Calc expert! A rectangle (positioned askew) inscribed in a right triangle, maximize area? http://www.thearealist.com/triangle-area/really-need-a-calc-expert-a-rectangle-positioned-askew-inscribed-in-a-right-triangle-maximize-area http://www.thearealist.com/triangle-area/really-need-a-calc-expert-a-rectangle-positioned-askew-inscribed-in-a-right-triangle-maximize-area#comments Tue, 06 Jul 2010 08:29:42 +0000 admin http://www.thearealist.com/triangle-area/really-need-a-calc-expert-a-rectangle-positioned-askew-inscribed-in-a-right-triangle-maximize-area A rectangle is to be inscribed in a right triangle having sides of length 6(ground leg), 8 (standing leg), and 10 in (hypotenuse). Find the dimensions of the rectangle with the greatest area assuming the rectangle is positioned with one side running directly on the hypotenuse (so like tipped up on one side). Need explanation! But any ideas will help.

This one is hard to explain in print. Let x be the side of the rectangle on the hypotenuse and y be the other side. There is a triangle formed at the right angle of the original which is similar to the original.
So x is to 10 as z is to 8: x/10 = z/8
and z = 4/5 x
The upper part of that leg would be 8 – 4/5 x

The triangle at the top is also similar:
So y is to 6 as (8 – 4/5 x) is to 10: y/6 = (8-4/5 x)/10
and y = 3/5 (8- 4/5 x) = 24/5 – 12/25 x

Now area = xy
Deriv = 0 and solve

]]> http://www.thearealist.com/triangle-area/really-need-a-calc-expert-a-rectangle-positioned-askew-inscribed-in-a-right-triangle-maximize-area/feed 2 What are the best July 4 fireworks shows in the Triangle Area? http://www.thearealist.com/triangle-area/what-are-the-best-july-4-fireworks-shows-in-the-triangle-area http://www.thearealist.com/triangle-area/what-are-the-best-july-4-fireworks-shows-in-the-triangle-area#comments Wed, 30 Jun 2010 16:23:51 +0000 admin http://www.thearealist.com/triangle-area/what-are-the-best-july-4-fireworks-shows-in-the-triangle-area What are the best fireworks shows that occur on 4th of July in or around the Triangle Area in North Carolina?

CHECK YOUR LOCAL PAPER

]]> http://www.thearealist.com/triangle-area/what-are-the-best-july-4-fireworks-shows-in-the-triangle-area/feed 1 How do i find the area of triangle knowing 3 sides? http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides-2 http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides-2#comments Mon, 28 Jun 2010 20:39:07 +0000 admin http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides-2 I know you have to take the sum of 3 sides first then use that to subtract each what you do next??
4. What is the area of triangle ABC if a=8,b=10, and c=15?
5. What is the area of traingle ABC if a=42, b=17, and c=25?

It’s called Heron’s formula:

http://www.mathopenref.com/heronsformula.html

What is the area of triangle ABC if a=8,b=10, and c=15?
SSS: SIDES: p= 8 , q= 10 , r= 15, area: 36.97888

What is the area of traingle ABC if a=42, b=17, and c=25?
SSS: SIDES: p= 42 , q= 17 , r= 25 Invalid combination of sides.

q+r = p
Area is zero.

]]> http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides-2/feed 1 how do i find the area of triangle knowing 3 sides? http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides#comments Fri, 25 Jun 2010 18:31:38 +0000 admin http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides I know you have to take the sum of 3 sides first then use that to subtract each what you do next??
4. What is the area of triangle ABC if a=8,b=10, and c=15?
5. What is the area of traingle ABC if a=42, b=17, and c=25?

It’s called Heron’s formula:

http://www.mathopenref.com/heronsformula…

What is the area of triangle ABC if a=8,b=10, and c=15?
SSS: SIDES: p= 8 , q= 10 , r= 15, area: 36.97888

What is the area of traingle ABC if a=42, b=17, and c=25?
SSS: SIDES: p= 42 , q= 17 , r= 25 Invalid combination of sides.

q+r = p
Area is zero.

]]> http://www.thearealist.com/triangle-area/how-do-i-find-the-area-of-triangle-knowing-3-sides/feed 1 How to find area and side length of triangle? http://www.thearealist.com/triangle-area/how-to-find-area-and-side-length-of-triangle http://www.thearealist.com/triangle-area/how-to-find-area-and-side-length-of-triangle#comments Mon, 26 Apr 2010 05:38:48 +0000 admin http://www.thearealist.com/triangle-area/how-to-find-area-and-side-length-of-triangle 2 questions i cant figure out ?

1. Find the side length of an equilateral triangle with an area of 36sqrt3

2. Find the perimeter of an equilateral triangle with a height of 7sqrt3.

please explain or give formulas or even a website that explains? thanks

The area of a triangle is bh/2. An equilateral triangle has some special properties that help us out.
Slice the equilateral triangle down the middle vertically, producing 2 30/60/90 degree triangles. If the base of the 30/60/90 triangle is x, then the hypotenuse (the original side of the triangle) is 2x, and the height is Sqrt(3)x. so the area of the equilateral triangle is the same as both of the 30/60/90 triangles, or x^2 Sqrt(3) where x is half the side of the equilateral triangle.

So x = 6 and the side of the equilateral triangle is 12.

2) If the height is 7sqrt(3) then teh base of teh 30/60/90 is 7, and the side is 14. 3 x 14 = 42

Grandpa

]]> http://www.thearealist.com/triangle-area/how-to-find-area-and-side-length-of-triangle/feed 2 Working out side of a triangle using given 2 sides and area? http://www.thearealist.com/triangle-area/working-out-side-of-a-triangle-using-given-2-sides-and-area http://www.thearealist.com/triangle-area/working-out-side-of-a-triangle-using-given-2-sides-and-area#comments Mon, 29 Mar 2010 00:01:47 +0000 admin http://www.thearealist.com/triangle-area/working-out-side-of-a-triangle-using-given-2-sides-and-area I have been given the triangle ABC.
AB=3.2cm
BC=8.4cm
The area of triangle ABC is 10cm²
There are no right angles.

Basically, I need to find the perimeter, so I need the missing side first.
Any ideas on how to do this would be greatly appreciated, thank you.

One standard formula for the area of a triangle is
Area = 1/2 a.c sinB
Here you are given the area, a and c, i.e. the area, AB and BC
So you have: 10 = 3.2 x 8.4 x sinB
sinB = 0.3720
You now have 2 sides and the included angle.
Use cosine formula to get side b.
b^2 = a^2 + c^2 – 2a c cosB
cosB = 0.9287 (convert from from sinB)
b^2 = 8.4^2 + 3.2^2 – 2 x 8.4 x 3.2 x 0.9287
b^2 = 70.56 + 10.24 – 49.93
b^2 = 30.87
b = 5.55
So the perimeter = sum of the 3 sides = 3.2 + 8.4 + 5.55 = 17.15
I am not claiming this is the shortest method.

]]> http://www.thearealist.com/triangle-area/working-out-side-of-a-triangle-using-given-2-sides-and-area/feed 1 What is the relationship between angles in a triangle and the resulting area of the triangle? http://www.thearealist.com/triangle-area/what-is-the-relationship-between-angles-in-a-triangle-and-the-resulting-area-of-the-triangle http://www.thearealist.com/triangle-area/what-is-the-relationship-between-angles-in-a-triangle-and-the-resulting-area-of-the-triangle#comments Wed, 17 Mar 2010 01:33:48 +0000 admin http://www.thearealist.com/triangle-area/what-is-the-relationship-between-angles-in-a-triangle-and-the-resulting-area-of-the-triangle 1. How does the size of an angle in a given triangle relate to the Area of the triangle?
2. How does the sin of an angle relate to the area?
3. When graphing the area of a triangle against Sin(theta), a straight line is produced. What does the slope and equation of this line mean?

Any help greatly appreciated.
Thanks, John.

1)area=1/2a*b*sin(C) where; a,b,C are lengths &angle of usual tri angle that is A propotional to c
2) area=1/2a*b*sin(C)
3) 1/2*a*b area of rectangula triangle

]]> http://www.thearealist.com/triangle-area/what-is-the-relationship-between-angles-in-a-triangle-and-the-resulting-area-of-the-triangle/feed 3 How do you find the area of a triangle using the determinant of a matrix, only working backwards? http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-a-triangle-using-the-determinant-of-a-matrix-only-working-backwards http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-a-triangle-using-the-determinant-of-a-matrix-only-working-backwards#comments Fri, 05 Mar 2010 01:38:49 +0000 admin http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-a-triangle-using-the-determinant-of-a-matrix-only-working-backwards Find x, such that the triangle has an area of 4.

(-5, 1), (0, 2), (-2, x)

Can someone please help me solve for x using a graphing calculator?
Thanks!

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

]]> http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-a-triangle-using-the-determinant-of-a-matrix-only-working-backwards/feed 1 Confused with this triangle area problem? http://www.thearealist.com/triangle-area/confused-with-this-triangle-area-problem http://www.thearealist.com/triangle-area/confused-with-this-triangle-area-problem#comments Thu, 25 Feb 2010 00:19:04 +0000 admin http://www.thearealist.com/triangle-area/confused-with-this-triangle-area-problem "The sum of the area of two triangles is 120cm^2. The triangles overlap to create another triangle, which is shaded. If 2/3 of the smaller triangle is unshaded, and 8/9 of the larger triangle is unshaded, what is the area of the shaded overlapping triangle?"

I tried to set up a system relating the two, but had two variables in one, and three in the other. Substitution only proved x = x for me. :p

Could someone get me started on the right path?

The part that is overlapping (shaded) is 1/3 of the smaller triangle, and 1/9 of the larger triangle.
S = area of the smaller triangle
L = area of the larger triangle

(1/3)S = (1/9)L
S = (1/3)L

You know that S + L = 120

By substitution, (1/3)L + L = 120
(4/3)L = 120
L = 90
S = 30

(1/3) of 30 = 10
(1/9) of 90 = 10

The overlapping area is 10cm²

]]> http://www.thearealist.com/triangle-area/confused-with-this-triangle-area-problem/feed 1 How to find area of triangle using vertices, and angles? http://www.thearealist.com/triangle-area/how-to-find-area-of-triangle-using-vertices-and-angles http://www.thearealist.com/triangle-area/how-to-find-area-of-triangle-using-vertices-and-angles#comments Thu, 18 Feb 2010 22:24:50 +0000 admin http://www.thearealist.com/triangle-area/how-to-find-area-of-triangle-using-vertices-and-angles Let be the triangle with vertices at P=(3,−2,1), Q=(−5,2,−5) and R=(3,−3,2).

The area of is:

The angle ∠QPR is _____ degrees
The angle ∠PQR is _____ degrees
The angle ∠PRQ is _____ degrees

14 degrees

23 degrees

97 degrees

]]> http://www.thearealist.com/triangle-area/how-to-find-area-of-triangle-using-vertices-and-angles/feed 1