Area List » triangle area http://www.thearealist.com Fri, 03 Feb 2012 07:36:48 +0000 http://wordpress.org/?v=2.8.4 en hourly 1 How do you find the area of triangle? http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-triangle http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-triangle#comments Tue, 10 Jan 2012 01:34:30 +0000 admin http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-triangle I know area of a triangle equals 1/2 base*height. But is is, Base times Heighf FIRST, then halve it, or is it half of the base first, then times the height?

That statement was a bit confusing, so here’s a second one in case you don’t understand the first one:
When finding the area of a triangle, do we divide the product of the base and height FIRST? Or do we calculate half of the base first, then multiply it by the height?

Thanks in advanced!

It doesn’t matter what you do first. You can multiply in any order. For instance, let’s say our base is 5 and our height is 2. Let’s look at it done every way:

5×2= 10
10x (1/2)= 5

2x (1/2)= 1
1×5= 5

5x (1/2)= 2.5
2.5 x 2= 5

Regardless of what you multiply first, you will always end up with 5.

]]> http://www.thearealist.com/triangle-area/how-do-you-find-the-area-of-triangle/feed 5 How to find Length of the base of a triangle if Area= 36 cm(sq’d) & base has a 90 degree angle? http://www.thearealist.com/triangle-area/how-to-find-length-of-the-base-of-a-triangle-if-area-36-cmsqd-base-has-a-90-degree-angle http://www.thearealist.com/triangle-area/how-to-find-length-of-the-base-of-a-triangle-if-area-36-cmsqd-base-has-a-90-degree-angle#comments Thu, 15 Sep 2011 08:41:08 +0000 admin http://www.thearealist.com/triangle-area/how-to-find-length-of-the-base-of-a-triangle-if-area-36-cmsqd-base-has-a-90-degree-angle Each angle of the triangle is labeled as follows beginning left to right beginning with base: X,Y,Z. Angle ‘Y’ is a 90 degree angle. The area of the triangle is 36 cm squared. Need to find the length of leg XY. Answers were: A. 6, B. 9, C. 12, D. 18, F. 24. Can anyone please explain in detail? Thanks!

insufficient data….

]]> http://www.thearealist.com/triangle-area/how-to-find-length-of-the-base-of-a-triangle-if-area-36-cmsqd-base-has-a-90-degree-angle/feed 3 Express the hypotenuse h of a right triangle given the area as a function of the perimeter? http://www.thearealist.com/triangle-area/express-the-hypotenuse-h-of-a-right-triangle-given-the-area-as-a-function-of-the-perimeter http://www.thearealist.com/triangle-area/express-the-hypotenuse-h-of-a-right-triangle-given-the-area-as-a-function-of-the-perimeter#comments Tue, 13 Sep 2011 00:31:31 +0000 admin http://www.thearealist.com/triangle-area/express-the-hypotenuse-h-of-a-right-triangle-given-the-area-as-a-function-of-the-perimeter Express the hypotenuse h of a right triangle with area 25m^2 as a function of it’s perimeter p.

How would I do this? Thank for helping!

Call A=25 the area.
Call a and b the sides (and their length) adjacent to the right triangle.

We have:
1) Area: A = ab/2, so that ab = 2A
2) perimeter: p = a + b + h, so that a+b = p – h
3) pythagoras: h^2 = a^2 + b^2

Now from (2):
(p-h)^2 = (a+b)^2 = a^2 + b^2 + 2ab
= h^2 + 2(2A) = h^2 + 4A, from the values from (1) and (3).

But (p-h)^2 = p^2 + h^2 – 2ph, so that:
p^2 + h^2 – 2ph = h^2 + 4A
p^2 – 2ph = 4A
2ph = p^2 – 4A
h = (p^2 – 4A) / (2p)

with A=25:
h = (p^2 – 100) / (2p)

]]> http://www.thearealist.com/triangle-area/express-the-hypotenuse-h-of-a-right-triangle-given-the-area-as-a-function-of-the-perimeter/feed 1 Software which will calculate the area under a graph? Or triangle area? http://www.thearealist.com/triangle-area/software-which-will-calculate-the-area-under-a-graph-or-triangle-area http://www.thearealist.com/triangle-area/software-which-will-calculate-the-area-under-a-graph-or-triangle-area#comments Sat, 03 Sep 2011 11:10:00 +0000 admin http://www.thearealist.com/triangle-area/software-which-will-calculate-the-area-under-a-graph-or-triangle-area Hi, I have 4 or so graphs to calculate the area of. I am willing to redraw them digitally.

Is there any software which will give me a numerical value for the area under the triangle of each graph?

Or the area of each triangle I draw?

Thanks.

http://www.easycalculation.com/area/triangle.php

]]> http://www.thearealist.com/triangle-area/software-which-will-calculate-the-area-under-a-graph-or-triangle-area/feed 2 Someone please help me with confused Trig Triangle Area question? http://www.thearealist.com/triangle-area/someone-please-help-me-with-confused-trig-triangle-area-question http://www.thearealist.com/triangle-area/someone-please-help-me-with-confused-trig-triangle-area-question#comments Sun, 28 Aug 2011 00:58:06 +0000 admin http://www.thearealist.com/triangle-area/someone-please-help-me-with-confused-trig-triangle-area-question So I am given the question. A triangular block of land has been surveyed and pegged out. Calculate the area of the triangle block of land using Trigonometry Please show working aswell

So the triangle looks like this / Left side 36.4m \ Right side 30.3m _ Bottom 48.5. All help appreciated

Awkward.

You have three sides, so you can find an angle using the cosine rule. With that angle you can calculate the height, then area, of the triangle.

a² = b² + c² – 2bc cosA
36.4² = 30.3² + 48.5² – 2(30.3)(48.5)cosA
1324.96 = 918.09 + 2352.25 – 2939.10cosA
-1945.38 = -2939.10cosA
A = inverse cos(0.6618…) = 48.55…

sinA = height of triangle / 30.3
height of triangle = 30.3 * 0.749… = 22.712…

area of triangle = ½ * base * height = ½ (48.5) (22.712…) = 550.783…

The area of your triangle is 551m² (nearest m²)

]]> http://www.thearealist.com/triangle-area/someone-please-help-me-with-confused-trig-triangle-area-question/feed 1 What is the area or perimeter of a triangle whose area and perimeter have the same numerical value? http://www.thearealist.com/triangle-area/what-is-the-area-or-perimeter-of-a-triangle-whose-area-and-perimeter-have-the-same-numerical-value http://www.thearealist.com/triangle-area/what-is-the-area-or-perimeter-of-a-triangle-whose-area-and-perimeter-have-the-same-numerical-value#comments Tue, 04 Jan 2011 02:42:43 +0000 admin http://www.thearealist.com/triangle-area/what-is-the-area-or-perimeter-of-a-triangle-whose-area-and-perimeter-have-the-same-numerical-value What is the area or perimeter of a triangle whose area and perimeter have the same numerical value and this value is a minimum with angles 44, 61 and 75 (all degree measures)? Give solution to 8 decimal places.
Max please check the last digit.

21.90390137

]]> http://www.thearealist.com/triangle-area/what-is-the-area-or-perimeter-of-a-triangle-whose-area-and-perimeter-have-the-same-numerical-value/feed 3 Do centroid divides any triangle area in three equal areas ? http://www.thearealist.com/triangle-area/do-centroid-divides-any-triangle-area-in-three-equal-areas http://www.thearealist.com/triangle-area/do-centroid-divides-any-triangle-area-in-three-equal-areas#comments Wed, 08 Dec 2010 20:52:10 +0000 admin http://www.thearealist.com/triangle-area/do-centroid-divides-any-triangle-area-in-three-equal-areas if yes prove it and if no then which point of triangle do this.
Thanks
Hey venkat R
Is this true for all types of Triangle ?

When the centroid is joined to the vertices of its triangle, it is true that the centroid divides the triangle into three equal areas. Proof: Let ABC be the triangle and O the centroid. Let AO produced meet BC in D. The Area of the triangles ABD = Area of triangle ACD. ( Reason BD=CD and same altitude. Area = 1/2*base*altitude) For the same reason Area OBD = Area OCD. Subtracting i.e

Area ABD – Area OBD = Area ACD – Area OCD which implies Area AOB = Area AOC. Similar proof leads to Area AOC = Area BOC. Therefore Area AOB = Area AOC = Area BOC. That meand the centroid divides any triangle into three equal areas

for picture click http://i26.tinypic.com/2r47xtz.gif

]]> http://www.thearealist.com/triangle-area/do-centroid-divides-any-triangle-area-in-three-equal-areas/feed 1 I have three linear equations & they form a triangle, how do i find the triangles area? http://www.thearealist.com/triangle-area/i-have-three-linear-equations-they-form-a-triangle-how-do-i-find-the-triangles-area http://www.thearealist.com/triangle-area/i-have-three-linear-equations-they-form-a-triangle-how-do-i-find-the-triangles-area#comments Tue, 30 Nov 2010 01:18:43 +0000 admin http://www.thearealist.com/triangle-area/i-have-three-linear-equations-they-form-a-triangle-how-do-i-find-the-triangles-area I also have the intercept points.
I have to use the information above (equations and intercepts) to find the area.
Help please!
The equations are y=2x+2, y= -x+5 and y=1/2x-1
the intercepts are (1,4) (-2,-2) and (4,1)

First take the distance between each intercept:
d = sqrt((second x – first x) ^2 + (second y – first y)^2)

So the distance between (1,4) and (-2,-2) would be:
sqrt((1+2)^2 + (4+2)^2)
sqrt(45)

You get a triangle with sides:
sqrt(45), sqrt(18), and sqrt(45), and since it has two sides that are equal it’s an Isosceles Triangle.

To make things easier (slightly), I’m just going to use the area formula for an Isosceles Triangle:
A = (1/2)*base^2*sqrt((side^2/base^2) – (1/4)
A = (1/2)*sqrt(18)^2*sqrt((sqrt(45)^2/sqrt(18)^2) – (1/4))
A = (1/2)*18*sqrt((45/18) – (1/4))
A = 9*sqrt(1.1)

Please note that this answer is only correct if the intercepts you gave are correct (I didn’t check them) as it needs the triangle to have two equal sides.

]]> http://www.thearealist.com/triangle-area/i-have-three-linear-equations-they-form-a-triangle-how-do-i-find-the-triangles-area/feed 2 How to find the sides of a triangle given the area and 3 angles? http://www.thearealist.com/triangle-area/how-to-find-the-sides-of-a-triangle-given-the-area-and-3-angles http://www.thearealist.com/triangle-area/how-to-find-the-sides-of-a-triangle-given-the-area-and-3-angles#comments Wed, 10 Nov 2010 10:01:33 +0000 admin http://www.thearealist.com/triangle-area/how-to-find-the-sides-of-a-triangle-given-the-area-and-3-angles An isosceles triangle has an area of 24 cm2, and the angle between the two equal sides is
5pi/6. What is the length of the two equal sides?

The length of the two equal sides is approximately equal to 23 cm….
Too much working out….

]]> http://www.thearealist.com/triangle-area/how-to-find-the-sides-of-a-triangle-given-the-area-and-3-angles/feed 2 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