Can You Solve this 6th Grade Geometry Problem From China?

[cirr]

Can You Solve this 6th Grade Geometry Problem From China?

By Johannes Van Zijl on August 24, 2016

photo credit: Screen capture from video by MindYourDecisions

What is the total area of the red spots?

Here’s a new geometry problem by MindYourDecisions.

You start with a rectangle that’s 10 by 20 in dimensions. Two corners of the rectangle are connected with a diagonal line. There are also two circles of equal size inside the rectangle that are tangent to each other and tangent to the rectangle.

See if you can find the total area of the red spots.

Give the problem a try; it was supposedly asked to 6th graders in China. Can you figure it out?

http://thescienceexplorer.com/universe/can-you-solve-6th-grade-geometry-problem-china

 

[A_Poster]

Can You Solve this 6th Grade Geometry Problem From China?

By Johannes Van Zijl on August 24, 2016

photo credit: Screen capture from video by MindYourDecisions

What is the total area of the red spots?

Here’s a new geometry problem by MindYourDecisions.

You start with a rectangle that’s 10 by 20 in dimensions. Two corners of the rectangle are connected with a diagonal line. There are also two circles of equal size inside the rectangle that are tangent to each other and tangent to the rectangle.

See if you can find the total area of the red spots.

Give the problem a try; it was supposedly asked to 6th graders in China. Can you figure it out?

http://thescienceexplorer.com/universe/can-you-solve-6th-grade-geometry-problem-china

Quite an easy problem for 6th grade level.

Area of rectangle= 20X10 =200 units

Area of Circles = 2 X Area of single circle = 2 X (22/7) X 25 = 157.14

Area not covered by circles = 200 - 157.14 = 42.86

Since area is symmetric about diagonal, therefore area covered by red coloured portion is half of total area not covered by circles.

i.e. 42.86/2 = 21.43 Ans.

 

[war&peace]

Total red area is 21.46018366025517 units

Quite an easy problem for 6th grade level.

Area of rectangle= 20X10 =200 units

Area of Circles = 2 X Area of single circle = 2 X (22/7) X 25 = 157.14

Area not covered by circles = 200 - 157.14 = 42.86

Since area is symmetric about diagonal, therefore area covered by red coloured portion is half of total area not covered by circles.

i.e. 42.86/2 = 21.43 Ans.

It is wrong to use 22/7 as the value of Pi as it introduces 0.040249943477070081 % of error in calculations that can propagate.

 

[Jf Thunder]

Total red area is 21.46018366025517 units



It is wrong to use 22/7 as the value of Pi as it introduces 0.040249943477070081 % of error in calculations that can propagate.

our "Numerical Methods" teacher taught us that the hard way

 

[war&peace]

our "Numerical Methods" teacher taught us that the hard way

Teachers in developing countries normally are good at making seemingly simple things hard. But I know what you are referring, it is the fan like propagation of error.

 

[Jf Thunder]

Teacher in developing countries normally are good at making simple things hard. But I know what you are referring, it is the fan like propagation of error.

he made us do 20 steps of the question, and then showed us the massive error it caused
He made us solve the 20 stepped question for both the value of "pi" stored in the calculator, and for 22/7

 

[bobsm]

2x π r² (r=5); 20X10= 200 => (200-50π)/ 2

 

[Thorough Pro]

very simple
total red area = ((10x20)/2)-area of circle (pie r square), r=10

Can You Solve this 6th Grade Geometry Problem From China?

By Johannes Van Zijl on August 24, 2016

photo credit: Screen capture from video by MindYourDecisions

What is the total area of the red spots?

Here’s a new geometry problem by MindYourDecisions.

You start with a rectangle that’s 10 by 20 in dimensions. Two corners of the rectangle are connected with a diagonal line. There are also two circles of equal size inside the rectangle that are tangent to each other and tangent to the rectangle.

See if you can find the total area of the red spots.

Give the problem a try; it was supposedly asked to 6th graders in China. Can you figure it out?

http://thescienceexplorer.com/universe/can-you-solve-6th-grade-geometry-problem-china

 

[war&peace]

very simple
total red area = ((10x20)/2)-area of circle (pie r square), r=10

Whenever people say very simple they make a simple mistake
the radius of circle is r = 5 units
10 is the diameter if you use r =10 the area of the red spot will be negative (-57.07963267948966)

he made us do 20 steps of the question, and then showed us the massive error it caused
He made us solve the 20 stepped question for both the value of "pi" stored in the calculator, and for 22/7

So what did he/she do during that time...call his/her friends or take a tea break?

 

[ChineseTiger1986]

My own quick solution:

(20 * 10 / 2) - (5^2 * pi)

 

[Place Of Space]

100-25π

 

[ashok321]

http://www.gzhphb.com/article/28/286847.html

 

[Jf Thunder]

So what did he/she do during that time...call his/her friends or take a tea break?

walking around the class, going out one door, and suddenly coming in through the other........
but fortunately that was the only question we solved during the whole class

 

[Maira La]

http://www.gzhphb.com/article/28/286847.html

Look carefully - the shaded area differs (slightly) form the one in the OP.

Edit: try this guys..

 

[kankan326]

10x10-π5x5=21.5