Maths Puzzle

[imhotep]

An old puzzle in circulation again. Calculate the shaded area. ABCD is a square with sides 4 cm.

 

[Stimulus mind]

 

[AEG]

(1/4 × 22/7 × 2^2) + (1/2 × 22/7 × 1^2) - 2^2

 

[07sanjeewakaru]

Using integration...?

 

[imhotep]

Using integration...?

Sure you can. But there's a geometrical solution.

PS: Using the areas of triangles and circle sectors.

 

[07sanjeewakaru]

Using integration...

Sure you can. But there's a geometrical solution.

Wow..

 

[gamaya80]

An old puzzle in circulation again. Calculate the shaded area. ABCD is a square with sides 4 cm.

You can intrigate and find the area easily

 

[wissnshaftler]

ඕක බාර්ඩ් ට දීලා හදාගමු

 

[MrFrog]

TFS. free welawaka balanna ona.
Monday is not the best day for this

 

[dilann]

You can intrigate and find the area easily

easily ? sure da ?
poddak try ekk dipn.

 

[Ritigala Jayasena69]

 

[Devendora_San]

 

[imhotep]

View attachment 227727

Appreciate your effort. However, you are making a wrong assumption. There are no four quarter circles involved. Think again.

Tip :

If you fix the origin at B (lower left corner), this is the area between two circles.
Circle 1 - Centre at E with radius 2 Equation (x-2)^2 + y^2 = 4
Circle 2 - Centre at A with radius 4 Equation x^2 + (y-4)^2 = 16

You can use an integral to arrive at the answer. However, you can calculate it without calculus by triangles and sectors.

 

[dilann]

Appreciate your effort. However, you are making a wrong assumption. There are no four quarter circles involved. Think again.

ලස්සන උත්තරයක් එනවද ?

 

[MCG12345]

{((π(4)^2)/4)-(2*2)-(2*4-(π(2)^2)/2)}/2 = 3.42477796

 

[Reincarnator]

 

[dilann]

{((π(4)^2)/4)-(2*2)-(2*4-(π(2)^2)/2)}/2 = 3.42477796

ඔහොම කැත උත්තරයක් තමයි ආවේ අනුකලනය කරන්න ගියාම.. මම අයින් කරල දැම්ම ලස්සන උත්තරයක් නැති නිසා.

 

[imhotep]

ඔහොම කැත උත්තරයක් තමයි ආවේ අනුකලනය කරන්න ගියාම.. මම අයින් කරල දැම්ම ලස්සන උත්තරයක් නැති නිසා.

It's close but not exactly right.... The answer is 3.84696

 

[Devendora_San]

Appreciate your effort. However, you are making a wrong assumption. There are no four quarter circles involved. Think again.

Tip :

If you fix the origin at B (lower left corner), this is the area between two circles.
Circle 1 - Centre at E with radius 2 Equation (x-2)^2 + y^2 = 4
Circle 2 - Centre at A with radius 4 Equation x^2 + (y-4)^2 = 16

You can use an integral to arrive at the answer. However, you can calculate it without calculus by triangles and sectors.

Not mine brother. I just asked ChatGPT4 to resolve it.

 

[MrFrog]

For me also the first thought was to use integration. but i cannot remember how to do that. haven't used integration in around 20 years

geometric widiyata haduwa. (Sector 1 - triangle 1) + (sector 2 - triangle 2). Answer eka awe 3.9355. may be I made mistakes in the calculations.