Very interesting sum Thanks a lot

@PreMath

Жыл бұрын

Glad you think so! Thanks for your feedback! Cheers! You are awesome, Mohan. Keep smiling👍 Love and prayers from the USA! 😀

As usual, here's a slightly different approach: Area of yellow triangle = 35. Let the height of this triangle (sideways) be x. Then 35 = (1/2)(x)(3√14) = (3x√14)/2. Solving for x: x = (35)(2)/(3√14) = 70/(3√14) = (70√14)/42 = (35√14)/21 = (5√14)/3. Now the altitude (sideways) of the blue triangle is 3√14 - x: 3√14 - (5√14)/3 = (9√14)/3 - (5√14)/3 = (4√14)/3; and the area of the blue triangle is (1/2)((4√14)/3)(3√14) = ((2√14)/3)(3√14) = 2(√14)^2 = (2)(14) = 28. Carpe Diem. 🤠

@MrPaulc222

Жыл бұрын

Pretty much how I did it.

@DanielNeedham2500

Жыл бұрын

Same here

@heptamusica7745

Жыл бұрын

Elemental

@BeastModeWorkout24

5 ай бұрын

I solved in the same way

@AmirgabYT2185

Ай бұрын

I solved it the same way 😁

If the area of the yellow triangle is 35cm² and knowing that its base is the side of the square (3√14cm) then its height is 5√14/3cm. Therefore the height of the blue triangle is 4√14/3cm. Consequently; Area of the blue triangle= 1/2×4√14/3cm×3√14cm= 28cm²

Les hauteurs des triangles jaunes et bleus font au total la longueur du carré, donc la somme des aires des 2 triangles est égale à la moitié de 3*sqrt14 au carré donc 63, alors l'aire du triangle bleu est égale à 63-35 donc 28

@PreMath

Жыл бұрын

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

@yveslecoadou

Жыл бұрын

bien vu ! :)

@SrisailamNavuluri

Жыл бұрын

Sorry I did not understand your language.

Move the meeting point of all triangles straight down until it touches the square. Yellow and teal areas don't change. Green disappears. Red is half the total 1/2*(3sqrt(14))^2 = 63, deduct 35 and you're left with 28 for the teal.

@PreMath

Жыл бұрын

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

تمرين جميل جيد . رسم واضح مرتب . شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا . تحياتنا لكم من غزة فلسطين .

Thank you for video. I observed that sum of heights of blue & yellow is the side length of the square. The base of these trianlges is side length of square too. Their total area is (1/2)(9)(14) = 63. So 63 -35(yellow) = 28 being area of blue triangle.

Área del cuadrado =9×14=126 》》 Bajamos verticalmente el vértice interior común hasta la base y el cuadrado queda dividido en tres triángulos, uno azul y otro amarillo de áreas equivalentes a los del esquema inicial; el tercero tiene una superficie igual a la suma del verde y del rosa; superficie que equivale a la mitad de la del cuadrado 》 Azul + Amarillo = 126/2=63 》Azul =63-35 =28 Gracias y un saludo.

I reverse calculated the height of the yellow triangle from the area of 35 to be 5/3*√14, then the height of the blue triangle becomes 4/3*√14 Area of the blue triangle =1/2 * 3√14 * 4/3*√14=28 square units

@Copernicusfreud

Жыл бұрын

That was my method too. h of blue triangle is 3* (sq rt (14)) - 5/3 * (sq rt (14))

Amazing. Very well explained

Got it!!!! Amazing solution... Found it easy as the video progresses

Brilliantly simplified 👍 Solutions shared in comments are equally good.

Very awesome mind! I thought it could be longer solution, but before i know it, the answer was there slapping my face, saying i’d better wake up!

Amazing👍 Thanks for sharing 😊

Yay! I solved the problem.

Too easy. Thanks Professor!🥂👍❤

I love how you demonstrated solving this problem in simple terms.

Here's how I did it in my head. We have a perfect square divided in to four triangles by the corners, with each triangle being unknown. We can know that pink + green = blue + yellow, and we're given that the area is (3√14)^2, becoming 9*14. Since we have two equal segments, we can say that blue + yellow = 9*14 / 2 = 9*7. Knowing that yellow = 35, we can say that Blue + 35 = Blue + 5*7 = 9*7, and therefore Blue = 9*7 - 5*7 = 4*7, so therefore the area of Blue is 28 cm^2

excellent guru (sir) very beautifull

Super ! Je vais pouvoir le donner en exercice à mes élèves ;) Merci !

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

Nice resolution ! I did it a different way, based on the formula of the area of a triangle (1/2*base*height). I have labelled the height of the blue triangle ´h’. The height of the yellow triangle is then 3*sqrt(14)-h. Therefore the area of the yellow triangle (35) equals to 3*sqrt(14)*(3*sqrt(14)-h)*1/2. After developing, I obtained h=56/(3*sqrt(14)). The area of the blue triangle can be calculated : (3*sqrt(14)*56)/(2*3*sqrt(14))=28cm^2

¡Precioso ejercicio!

Good. I solved it by an other technique

There is a much easier solution. The height of the yellow (Hy) and blue (Hb) triangles added together is equal to the length of a side of the square (S). So calculate Hy from the known area and known leg of yellow triangle. Hb then = S - Hy and now we can compute the area of the blue triangle using it's known leg (S) and known Hb.

area of blue triangle + 35 = area of square /2 area of blue triangle = 9x14/2 -- 35 = 28

@PreMath

Жыл бұрын

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

@anibalarostegui5574

Жыл бұрын

The heights of yellow and blue triangles are on line, so knowing the base of yellow triangle (the length of the side of square) and its area, we can calculate its height("h") as: [ A=(b×h)/2 => h=(A×2)/b ], then the height of the blue triangle is the length of the side of square(parallel to the heights because has the same perpendicular) less the height of yellow triangle, so knowing the height and the base (side of square too), now we're able to calculate its area. ¡Done! 😑😜😋🙃🤩 - 🇦🇷⭐⭐⭐ -

😂😂😂😂😂😂 What a simple 'trick!' And here I was thinking, "Men!! How do we solve this one?!!" Thank you PreMath

Thank u 🎉

A= 0,5×(3√14)^2- 35= 7×4= 28 cm^2 Thanks sir!

I JUST SOLVED THE MATH. BUT, BY ANOTHER PROCESS

Got it. I solved for height of the 35cm^2 triangle, used the difference as the height of the other. Got 28 for its area.

I would say that it is easyer to get the height of the known triangle , since it´s surface is base times height divided into 2, Since its surface is 35 units squared, its height must be 2* (35/3 sqrt(14). so, the height of the unknown triangle is 3 sqrt(14) - height of known triangle. And easyly multiply this new height by the square lenght and divide this result by 2

Thanks a lot sir!That was a really creative solution which has appealed to me;however,it strikes me that this question owns another solution as well!As long as you look into this system more carefully,you will expressly realize that it may help to draw and calculate the height of yellow triangle, which turns out to equal five-thirds times the square root of fourteen; and then you can easily subtract this amount from the total side of this square and finally reach the blue square's height, which can comfortably gives the area of the blue square depicted on the clip making use of the basic formula to compute a triangle's area, which is equivalent to 28!How do you evaluate this remedy;I truly reckon that this would be much more convenient,wouldn't be!😊

I used a different method. s is 3*sqrt(14). x is the width of the yellow triangle. x * s = 70 x = 70 / s The area, a, of the teal triangle is a = (s - x) / 2 * s 2a = (s - x) * s 2a = (s - (70 / s)) * s 2a = s*s - 70 2a = 126 - 70 = 56 a = 28

In such divisions, the total area of opposite triangles would be equal. (Areas of pink + green = yellow + blue) All triangles here have equal bases (b = 3_/14). If the height of the pink triangle is h1 and that of the green triangle is h2, their areas would be. ½ bh1 and ½bh2 respectively. Adding these would be ½b(h1+h2). But, h1+h2 is equal to the base. So, the area of these triangles would be ½b*b = ½* (3_/14)*(3_/14) = ½* 126 = 63 The total area of the yellow and blue triangles would also be 63. The area of blue triangle would be 63 - 35 = 28.

Notice that the sum of the areas of the 2 opposite triangles are equal= 1/2 the area of the square (Pink+Green=Blue+Yellow) So x+ 35=63 x= 63-35=28 sq cm

I see that sum of blue triangle and yellow triangle is half of the square. 126/2=63, 63-35=28

It can be solved simply by observing that the area of a triangle is half of the rectangle it is inscribed in. Hence blue triangle area = ½(Area of square - 2*YellowTriangle)= 28

شكرا يمكن استعمال صيغة القاعدة والإرتفاع في المثلث الازرق وفي المثلث الأصفر مجموع الإرتفاعين هو ضلع المربع نجد بسرعة 28

Different way to calculate it. Start with the formula for the area of a triangle, bh/2 The known triangle, then has a base of 3√14 and a height of 70/(3√14) The unknown triangle has a height of (3√14)-(70/(3√14) (3√14)((3√14)-(70/(3√14)))/2 ((9×14)-70)/2 (126-70)/2 56/2 28 Same basic idea and ending steps, but done without the congruent triangles

can you find length of the other sides of the yellow triangle ?

Area of green ∆le=1/2(3√14)h1=35 Area of blue ∆le=1/2(3√14)h2=x+y Adding/2(3√14)(h1+je)=35+x+y Here h1+h2=3√14 x+y+35=1/2×9×14=63 x+y=63-35=28 Or Sum of the areas of blue and yellow=sum of the areas of other two triangles=1/2(3√14)^2=9×14/2=63 Blue area +35=63 Blue area =63-35=28.

An in-the-head quickie. Spoiler alert. The area of opposite triangles must add up to half the square's area. (3√14)² = 9 ∙ 14 = 126. 126 / 2 = 63. Blue area = 63 − 35 = 28 square units. Now to watch how I should have done it.

3√14 =11.22 1/2 ×11.22× h1=35 h1=35÷5.61=6.24 h2=11.22 - 6.24= 4.98 Area= 1/2 ×11.22 ×4.98=27.94

area of the square = side x side = 126. yellow + blue = half of square = 63. So blue = 63-35=28

Pink+green=1/2(3sqrt14)^2=63... Blue=9*14-63-35=28

S=28

My solution: j is height of green ∆ k is height of pink ∆ k + j = 3√(14) Area of blue ∆ = Area of square - (area of pink ∆ + area of yellow ∆ + area green ∆) Area of square = (3√(14))² = 126 Area of pink ∆ = ½k3√(14) Area of green ∆ =½j3√(14) Area of yellow ∆ = 35 Therefore area of blue ∆ = 126 - (½3√(14)(k + j) + 35) = 126 - ½(3√(14))² - 35 = 126 - 63 - 35 = 28 cm²

You know math as art rather than just remembering the rules as a science.

Seems not too difficult, the sum of area of blue and yellow triangles is half of that of the area=126/2=63, so the answer is 64-35=28, done.😊

For each side of the square "a" the answer is "a.a/2-35". Why is this square root?

x + 35 = 3√14 * 3√14 * 1/2 = 63 x = 28 Area of the Blue Triangle : 28cm²

(((3×14^(0,5))-(70÷126^(0,5)))×3×14^(0,5))÷2

Square=(3sqrt14)^2 Square=126 126/2-35=Blue 63-35=Blue 28=Blue

Won’t the sums of the blue and yellow triangles alway be 1/2 of the square? 126/2 is 63. 63 minus 35 is 28.

Gg