A Parallelogram Meets An Equilateral Triangle
Find the area of the shaded(yellow) part.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
9 solutions
Area Of BEGH = (Area Of Triangle BEF) - (Area of Triangle HGF) = (1/2(12) 6√3 ) - (1/2 (2) √3 ) = 35√3
Area Of Triangle BCH = (Area Of BEGC ) - (Area Of BEGH) = (12*5√3) - (35√3) = 25√3
Area Of AEGD = 3 * 5√3 = 15√3
Area Of Yellow Parts = (Area Of BCH) + ( Area Of AEGD) = 25√3 + 15√3 = 40√3 ^_^
good sir
thnks.. good sir
AE = AB-AE = 15 - 12 = 3 cm > AE = DG EG = EF - EG = 12 - 2 = 10 cm >AD = EG = BC = HB
Triangle HBC is an equilateral triangle Area of HBC = [√3/4]x10x10 = 25√3
Parallelogram ADGE can be divided into 2 triangles Area of Triangle ADE = Area of Triangle DGE
Area of Parallelogram ADGE = [10 x 3 x sin(60)] = 15√3
Shaded Area = 25√3 + 15√3 = 40√3
Answer = 40√3
Good
I THINK IT IS 69.28 SQUARE UNITS.
A=bh, h=perpendicular from d, b=line segment AB=15....., m/_DAB=60degrees=>h=2 AD/root of 3=20/root 3 Area=15 20/root 3=100*root 3...... please verify your answer
I was wondering why triangle FGH is equilateral....the answer is due to similarity of triangles.This also means any equilateral triangle lopped of by a line parallel to the base of the original would be automatically equilateral.
150-.5 12 6 1.732+.5 2*1.732=??
I forgot just the shaded orange...
AE = AB-AE = 15 - 12 = 3 cm > AE = DG EG = EF - EG = 12 - 2 = 10 cm >AD = EG = BC = HB
Triangle HBC is an equilateral triangle Area of HBC = [√3/4]x10x10 = 25√3
Parallelogram ADGE can be divided into 2 triangles Area of Triangle ADE = Area of Triangle DGE
Area of Parallelogram ADGE = [10 x 3 x sin(60)] = 15√3
Shaded Area = 25√3 + 15√3 = 40√3
Answer = 40√3
Why is stated that ABCD is a parallelogram or that FG = FH = GH = 2 if it was never stated that AB and DC were parallel lines?
Why BEGH= 1/2 (12+2) 5√3
Log in to reply
5√3 is the height of the parallelogram, and (12+2) / 2 is to get the average of the bases of the trapezoid (FG = 12 and FG - EG = 2 and since the triangle is equilateral by similar triangles, the bases are 12 and 2) to get the gray area overlapping the parallelogram.
BE=BF=EF= 10+2 = 12. So, FG=FH=GH= 2. Height of ABCD = height of BEGH = √12^2 - 6^2 - √2^2 -
1^2 = 6√3 - √3 = 5√3. The area of BEGH = 1/2 (12+2) 5√3 = 35√3. The area of ABCD = 15 x 5√3 =
75√3. So, the area of shaded orange = 75√3 -35√3 = 40√3
Y e l l o w a r e a s i s a p a r a l l e l o g r a m a n d a n e q u i l a t e r a l t r i a n g l e . F i r s t , w e k n o w t h a t ∠ D A B = ∠ G E B = 6 0 ⋅ . A n d t h a t A D = E G = C B = B H = 1 0 c m . T h e n , w e c a l c u l a t e h e i g h t o f p a r a l l e l o g r a m A B C D . h = 1 0 × sin ∠ D A B = 5 3 . T h e n , w e k n o w t h a t o n e s i d e o f △ F E B i s 1 2 c m a n d A B i s 1 5 c m , s o A E = 3 c m . S o t h e a r e a o f A D G E i s ( 3 ) × ( 5 3 ) a n d t h e a r e a o f t r i a n g l e B H C i s ( 1 0 ) × ( 5 3 ) . F i n a l l y , t h e a r e a o f y e l l o w p a r t i s △ F E B + A D G E = 4 0 3 .
height of parallelogram = 10 x sin60 area of parallelogram = 150 x Sin60
area of full triangle = 1/2 x 12 x 12Sin60 = 72 x sin60
area of top secton of triangle = 1/2 x 2 x 2 sin60 = 2 x sin60
area of triangle inside parallelogram = 70 sin60
area of yellow part = 80 sin60
by simple method of area we can calculate the answer which is equal to 40*3^1/2
area of short parallelogram 15 3^(1/2)+area of triangle BCH is 25 3(1/2) then total is 40*3^(1/2)
area of EGHB is 50root3; area of CHB(equilateral) is 25root3; area of EBF is 36root3; area(ADE+BHC) = area(BHC)+area(ADHB)-{area(EFB)-area(GHF)}
one first find the perpendicular distance b/w the two // lines AB and CD and then find the area from //gm formula bxh and 1/2 x b xh.
tnx buddy
BE=BF=EF= 10+2 = 12. So, FG=FH=GH= 2. Height of ABCD = height of BEGH = √12^2 - 6^2 - √2^2 - 1^2 = 6√3 - √3 = 5√3. The area of BEGH = 1/2 (12+2) 5√3 = 35√3. The area of ABCD = 15 x 5√3 = 75√3. So, the area of shaded orange = 75√3 -35√3 = 40√3