Find the area of the shaded portion in the equilateral triangle with sides 6.
(assuming the central point of each arc is its corresponding vertex)

help me please

Question

Find the area of the shaded portion in the equilateral triangle with sides 6.
(assuming the central point of each arc is its corresponding vertex)

help me please

anonymous · Answer

attachment

anonymous · Answer

its supposed to be a diff diagram ughh its not showin up

anonymous · Answer

Damn cherri you have been asking this from quite a long time sorry but i can't help at this but I will get you help

anonymous · Answer

yeah its cus i got it reassign by my teacher

akshay_budhkar · Answer

whats the area of a sector? i dun remember the formula..

hero · Answer

I will try to help you solve it. It involves finding the area of a circle and area of the triangle

anonymous · Answer

yea hero is right

hero · Answer

And area of a sector too. The angle is 60 degrees across that sector

akshay_budhkar · Answer

the answer is 2(16*pie-4*root2)

akshay_budhkar · Answer

i guess so

akshay_budhkar · Answer

no i am wrong sorry

akshay_budhkar · Answer

what is the area of a sector guys??????

anonymous · Answer

angle is 60

anonymous · Answer

Come on, I told u this before, its twice the sector minus the triangle (equilateral)

anonymous · Answer

full area is pi16 divide by 6 we get sector area 16pi/6

amistre64 · Answer

the area of a sector of an angle that sweeps out 2pi; is ... (2pi r^2)/2

anonymous · Answer

now comes the part i hate calculate triangle area and subtract from sector

hero · Answer

Use Heron's formula to find the area of triangle

akshay_budhkar · Answer

area of triangle is 4root2

anonymous · Answer

Twice half the base*height.

akshay_budhkar · Answer

8 root2 sorry its twice

anonymous · Answer

Guys I already have the solution. Is on this post: http://openstudy.com/groups/mathematics/updates/4e36de0f0b8ba7b2da430abb

anonymous · Answer

Area of the triangle is $2\sqrt{12}$ ($6.928$). Took the base as 4, used pythagoras to get the height (divided the triangle into 2 right-angled triangles). Area of the sector is $\frac{1}{6}\pi 4^{2}$ ($8.378$). Area of 1 segment is the difference: ($1.450$), area of the highlighted area is twice that ($2.900$).

phi · Answer

If all else fails, http://en.wikipedia.org/wiki/Circular_segment Here we know theta= pi/3 , R= 4, and we want to double the area of the segment (because the formula just gives us half the area in the problem).

anonymous · Answer

The easiest way to do these things if the problem allows it is to use circle figures so

its twice the area of the circle less the area of the hexagon (3sqrt(3)/side^2)

anonymous · Answer

3sqrt(3)/side^2 over 2 and take 1/6

hero · Answer

16.76 - 13.86 = 2.9 or approximately 3 units squared

anonymous · Answer

2* 1/6(pi 4^2 -3 sqrt 3 4^2/2)

Whatever that is....

hero · Answer

16.76 is the area of both sectors....13.86 is the area of both triangles

anonymous · Answer

2* 1/6(pi 4^2 -3 sqrt 3 4^2/2) Whatever that is....

= 2.898 approx (16pi/3 - 8 sqrt 3)

hero · Answer

Two different routes to the same answer

hero · Answer

I got the same thing you did, I just rounded

hero · Answer

Can I please get some credit for this....I spent a bit of time calculating the result, lol

hero · Answer

I didn't even realize Dalvaron had come up with the answer much earlier.

anonymous · Answer

Heh, the answer was there long beforehand, I just crunched the numbers :D