Think outside the Box | Calculate area of the Blue shaded Region in a rectangle

[@vara1499]

Great! I thought the solution would take many steps but you solved it a few steps. Thank you, out of box thinking has helped in finding a solution.

[@PreMath]

Excellent! Thanks for your feedback! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@vara1499]

@@PreMath I have a request. Please solve problems in Calculus, the subject I dreaded because of teachers who could not explain the basics clearly. Limit theory was/is a mystery even now. Thank you in advance.

[@SamsungJ-kk5nr]

Buena estrategia para resolver. No lo había visto como lo viste vos. Mi resolución era más larga.

[@HappyFamilyOnline]

Awesome 👍 Thanks for sharing😊😊

[@KAvi_YA666]

Thanks for video.Good luck sir!!!!!!!!!!!!

[@PreMath]

You are very welcome! Thanks for your continued love and support! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@ahmedrafea8542]

A really nice problem. Thanks

[@sandytanner9333]

Excellent!

[@batavuskoga]

At first I calculated the quarter circle on the right and then the remaining rest of this square on the rightn like shown in the video. And just before making the final calculation I realized I could do it like said in the video. That simple.

[@quigonkenny]

By observation, as the arc forming the right side of the left white figure and the arc forming the left side of the right white figure are congruent, the two white features combined make up a square of 7 units per side. Blue area is entire triangle minus white areas, so... A = 14(7) - 7(7) = 98 - 49 = 49

[@Copernicusfreud]

Yay! I solved it without a pen, a paper, or a calculator. I came up with 49/4*pi + (49 - 49/4*pi). Combining terms only leaves 49.

[@theoyanto]

Great, but sneaky, I knew it had to be simple because the video is only 3 minutes long. Thanks again 👍🏻

[@alster724]

That was quick and amazing I realized that the two squares are _mirror images_ of each other

[@mikefischer8067]

This is one of those where I simply saw the answer. The two white sections merge to form a 7 x 7 square, leaving 1/2 of the 14 x 7 rectangle for the blue region. Took two seconds literally.

[@TimBoulette]

49. Almost by inspection.

[@PreMath]

Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@roberteltze4850]

That was my thought except the shape of the curved lines was never defined. Are they arcs of a circle? If so do they have the same radius? They could follow some other equation where both curves don't actually intersect the rectangle until the upper right corner. It just bothers me when important information is left undefined.

[@izaiasmurati5499]

Interessante e fácil.

[@lk-wr2yn]

This was for me the easiest that you asked. If you see that the blue quater cycle is the white, than it is 7^2=49... Thanks

[@PreMath]

Excellent! Thanks for your feedback! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@bigm383]

Simple!❤🥂

[@PreMath]

Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@unknownidentity2846]

If we rotate the figure by 90°, we can regard the blue region as a region between two function f(x) and g(x). Therefore we can calculate the area also via Area = ∫(0,7) [f(x) − g(x)] dx = ∫(0,7) 7 dx = 7*(7−0) = 49 Best regards from Germany

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@devondevon4366]

49 Answer Divide the rectangle into two equal parts, forming two squares; the area of non -shaded region to the left is 7^2 - (22/28) 7^2. The area of the non-shaded region to the right is (22/28) 7^2. The total area of the non-shaded region is 7^2 - (22/28)7^2 + (22/28) 7^2 = 7^2 =49 I use 22/7 for pi and since hence 22/28 (or 22/7 * 1/4) for the quarter circle.

[@shadmanhasan4205]

If u divide the blue region into 2 parts, u can literally just fit the 2 parts together to form a square that is 7 units in length: Therefore, blue region = 7^2 = 49 units square.

[@philipkudrna5643]

Before watching: the area is 49 square units, as - if you separate the figure in two half’s, the right piece fits exactly into the empty space of the figure, resulting in a perfect square with a sidelengths of 7.

[@AmirgabYT2185]

S=(49(6-π))/2≈70,07

[@santiagoarosam430]

(14/2)×7=49 Gracias y un saludo.

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@khatharrmalkavian3306]

If you collapse the blue region you get a 7*7 square. 7 is half of the original 14, so the blue region is half of the area of the rectangle. 14*7/2=49.

[@bentels5340]

49. Figured it out in my mind when I realized that the rectangle is two 7x7 squares with their colored areas reversed...

[@gedi223]

Although I see the logic behind solving this problem, your comment that "This diagram may not be 100% true to scale" makes the solution invalid. You would have to have given the length value of either the shaded or unshaded side on the bottom as 7.

[@j.r.1210]

Yes -- all the easy or "instant" solutions to this problem are in fact based on *assumptions* about the key dimensions, not on unambiguous given conditions. E.g., that curve on the left looks like a quarter-circle, so it must *be* a quarter-circle. That's not really valid.

[@broytingaravsol]

simple one

[@PreMath]

Thanks for your feedback! Cheers! You are awesome. Keep smiling👍 Love and prayers from the USA! 😀

[@alexniklas8777]

A=49(4-π)/4+49π/4= 49×4/4=49

[@srinivasansundararajan456]

One white small piece = one small blue piece. Hence 7×7=49 is blue area

[@mohamadtaufik5770]

49, piece of cake

[@PreMath]

Excellent! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@izaiasmurati5499]

E a mesma área de um quadrado de 7 por 7.

[@wackojacko3962]

Piece of Pi Slice of Cake 😉

[@PreMath]

Yummy!

[@tipeon]

The most difficult thing was to remember the multiplication table 😅

[@PreMath]

Thanks for your feedback! Cheers! You are awesome. Keep smiling👍

[@terryendicott2939]

I just removed the blue region and slid the two white area together - bingo.

[@misterunknown8923]

exactly half of the rectangle. 98/2

[@Waldlaeufer70]

This is nothing but a "curved" square with a side length of 7 units: A = 7² = 49 square units

[@nomad7966]

49

[@giuseppemalaguti435]

Mi sembra 49,anche se il disegno non è chiaro

[@devondevon4366]

49

[@vidyadharjoshi5714]

49