Blue Bow Tie

Geometry Level 3

What is the area of the blue shaded region?


The answer is 30.

Bryan Sangtania by Bryan Sangtania , 23, Indonesia

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10 solutions

Bryan Sangtania
Apr 18, 2014

the area of shaded blue = 1/2 x 8 x 5 - 1/2 x 8 x 3 + 1/2 x 8 x 8,5 - 1/2 x 8 x 3 = 1/2 x 8 x (5 - 3 + 8,5 -3) = 4 x 7,5 = 30

16 Helpful 0 Interesting 0 Brilliant 0 Confused

Form the equation of all line joining points. Use integration in shaded region. Done !

Kevin Patel - 7 years, 1 month ago

My first answer was wrong because of 3,5. I thought it was a 3 and then 5. :)

Daryll Jose - 7 years ago

però i due lati opposti dell'area blu non sono paralleli come avevo implicitamente pensato io

Claudia Manotti - 6 years, 12 months ago

I could have solved this....BUT I was unable to recognize the number 3.5 (which was wrongly displayed as 3 , 5).......... :-(

Sankarshaṇ Joshi - 7 years, 1 month ago
Karishma Mahanta
Apr 25, 2014

Area of blue shaded part=[1/2x8x(3+2)-1/2x8x3]+[1/2x8x(3+2+3.5)-1/2x8x3]=[(4x5)-(4x3)]+[(4x8.5)+(4x3)]=[20-12]+[34-12]=8+22=30

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it in a different manner(rather complicated) and got it "30".My doubt is in the 2nd part of your eqn,that is, [1/2x8x(3+2+3.5)....].I think u have applied "1/2xbxh".If so,can u please explain how could we conclude the h=8.5??

V Vishnu Prasad - 7 years, 1 month ago
Rahul Ukey
Apr 26, 2014

area of middle triangle white region(1/2x3x8)=12
are of first triangle blue region(1/2x(3+2)x8)-12 =8
area of second triangle blue region(1/2x(3+2+3.5)x8)-12 =22
total blue surface=22+8 =30


1 Helpful 0 Interesting 0 Brilliant 0 Confused
Krishna Garg
Apr 26, 2014

We first find out the heights of three triangles with given details. unshaded trianle is having height 3 so area of this trianle is 1/2X8X3 =12, Now height of left hand side triangle is 5 with base 8 ,so area of this trianle is 1/2 X8X5 =20, for shaded trianle it is 20 -12 =8, Similarly, for right side trianle base is 8 and height is 8.5 ,so area is 1/2X8X8.5 =22 So,for both shaded trianles(BOW so called) area are 22+8 +30 Ans, This Problem is very Tricky in deed due to proection of Geometry figure !!!

K.K.GARG,INDIA

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Abid Ali
Apr 24, 2014

the area of shaded region = (1/2 x 8 x 5 - 1/2 x 8 x 3) + (1/2 x 8 x 8,5 - 1/2 x 8 x 3) = 1/2 x 8 x (5 - 3 + 8,5 -3) = 4 x 7,5 = 30

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Miguel Domingo
May 1, 2014

8x8,5/2 + 8x5/2 - 2*(8x3/2)

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Mashiur Rafi
Apr 26, 2014

34+20-24=30

0 Helpful 0 Interesting 0 Brilliant 0 Confused

(8x5)/2-(8x3)/2+(8.5x8)/2-(8x3)/2

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Aliki Patsalidou
Apr 24, 2014

(8 8,5)/2-(8 3)/2 +(8 5)/2 - (8 3)/2

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Moshiur Mission
Apr 19, 2014

.5 8 3 = 12, .5 8 5 = 20, .5 8 8.5=34 1st blue part = 20-12 =8 2nd blue part = 34-12 = 22 so Blue Part total is 30

0 Helpful 0 Interesting 0 Brilliant 0 Confused

how did u solve this?

anandhan Thanappan - 7 years, 1 month ago

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Please see my solution to understand. K.K.GARG

Krishna Garg - 7 years, 1 month ago

what is the procedure? yar

Waqas Awan - 7 years, 1 month ago

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Please see my solution to understand.

Krishna Garg - 7 years, 1 month ago

that's how i finally got the correct answer

Linda Priddy-Hundley - 7 years, 1 month ago

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