Calculate area of the Blue shaded triangle | Important Geometry skills explained | Fun Olympiad

Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!

Need help with solving this Math Olympiad Question? You're in the right place!

I have over 20 years of experience teaching Mathematics at American schools, colleges, and universities. Learn more about me at

Calculate area of the Blue shaded triangle | Important Geometry skills explained | Fun Olympiad

Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!

#FindAreaOfBlueShadedTriangle #GeometryMath #MathOlympiad
#OlympiadMathematicalQuestion #HowToSolveOlympiadQuestion #MathOlympiadQuestion #MathOlympiadQuestions #OlympiadQuestion #Olympiad #AlgebraReview #Algebra #Mathematics #Math #Maths #MathOlympiad #HarvardAdmissionQuestion
#MathOlympiadPreparation #LearntipstosolveOlympiadMathQuestionfast #OlympiadMathematicsCompetition #MathOlympics #CollegeEntranceExam
#blackpenredpen #MathOlympiadTraining #Olympiad Question #GeometrySkills #GeometryFormulas #AreaOfTriangles #AreaOfRectangle #Quadrilateral #Rectangle
#MathematicalOlympiad #OlympiadMathematics #CompetitiveExams #CompetitiveExam

How to solve Olympiad Mathematical Question
How to prepare for Math Olympiad
How to Solve Olympiad Question
How to Solve international math olympiad questions
international math olympiad questions and solutions
international math olympiad questions and answers
olympiad mathematics competition
blackpenredpen
math olympics
olympiad exam
olympiad exam sample papers
math olympiad sample questions
math olympiada
British Math Olympiad
olympics math
olympics mathematics
olympics math activities
olympics math competition
Math Olympiad Training
How to win the International Math Olympiad
Po-Shen Loh and Lex Fridman
Number Theory
There is a ridiculously easy way to solve this Olympiad qualifier problem
This U.S. Olympiad Coach Has a Unique Approach to Math
The Map of Mathematics
mathcounts
math at work
Pre Math
Olympiad Mathematics
Two Methods to Solve System of Exponential of Equations
Olympiad Question
Calculate total Area of all shaded triangles
Geometry
Geometry math
Geometry skills
Right triangles
Square
imo
Competitive Exams
Competitive Exam

Subscribe Now as the ultimate shots of Math doses are on their way to fill your minds with the knowledge and wisdom once again.

[miguelgnievesl]

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

[williamwingo]

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. 🤠

[francismoles]

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

[szkoclaw]

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.

[engralsaffar]

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

[santiagoarosam]

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.

[spiderjump]

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

[normanc]

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.

[neologicalgamer]

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

[dawon]

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!

[MrYalti]

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

[MartinPollack-vh]

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.

[alster]

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

[kushanavahazariclassbroll]

I JUST SOLVED THE MATH.
BUT, BY ANOTHER PROCESS

[NASIRable]

Good. I solved it by an other technique

[misterenter-izrz]

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.😊

[reynaldowify]

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

[DB-lgsq]

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

[kinyutaka]

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

[SrisailamNavuluri]

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
Blue area +35=63
Blue area =63-35=28.