The pink triangle is a right triangle, so using the Pythagorean theorem, the height of the pink triangle is: sqrt (2^2 - 1^2) = sqrt (3).
Area of the triangle = base * height / 2 = 1 * sqrt (3) / 2 = sqrt (3) / 2.
The pink triangle is a right triangle, because both yellow triangles are equilateral triangles (1,1,1) and (2,2,2), which constrains them to be equi-angular, too. The sum of all angles in a triangle is always 180, and an equilateral triangle has angles of (60,60,60). The straight line, ABC, displays an angle of 180 degrees. Thus, angle EBD is 60 degrees. Cos (EBD) = 0.5, but only if the pink triangle is a right triangle. As we can see, (BD)/(EB) = 0.5, so the Cos works and the pink triangle is, indeed, a right triangle.
ABE and BCD are equilateral triangles, therefore AE and BD are parallel to each other. This makes ABDE a trapezoid. Area of BDE is : area of ABDE minus area of ABE, hence 0.5 *(2+1)*2*sin60 - 0.5*2*2*sin60 =3*sin60 - 2*sin60 = sin60= 0.866 which is also (sqrt(3))/2 .
ABC being a straight line then all angles at point b add up to 180. Angle ABE=Angle DBC=60 degrees since both are angles of an equilateral trianlge.
Therefore, angle EBD= 180 - (60+60)= 60 degrees.
Using the formula: Area= 1/2 ab sin C where a=BE=2 and b=BD=1 and C=angleEBD=60 degrees, the area thus becomes:
1/2 X 2 X 1 X sin60 = 1.7321 sq. units.
Working on the maths I was taught at school in the latter half of the last century, I was able to correctly calculate the area! But then I was using Pythagoras' theory-going back to the ancient Greeks! Tony
the simple answer is(total area-the area of rest two triangles )
by Christopher Wanamaker 11 years ago
Imagine a cake in the shape of an equilateral triangle as shown in the image below. Each side of thetriangle cake measures exactly 8 inches. What is the length of the shortest possible cut that will divide the cake into two pieces with equal area?
by Melanie Palen 14 years ago
I have blue triangles by a few of my hubs and I am wondering what they mean.For example this one:http://hubpages.com/hub/Meta-Data-for-SEO
by Misbah Sheikh 3 years ago
I was checking my account stats where I saw 2 high traffic signs on a single article, I mean 2 red arrows heading up, what does it mean? Is it a glitch or it means something different?
by Susan Reid 12 years ago
by Missy 11 years ago
I am a complete newb to HP and when checking my stats today saw a little blue triangle next to one of my hubs, so I see this means traffic has dropped, but can i get penalised for it? Or will the hub stop being featured?Im just unsure what it means?thanks
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Just checked the account and we are having a blue triangle morning. Is it something we said? Why can't the HubPages genius team think of something consoling for these down days? A little note along the lines "cheer up it won't last" might ease the pain.
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