Find area of the Green Square | All given shapes are squares| Important Geometry skills explained

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

Find area of the Green Square | All given shapes are squares| Important Geometry skills explained

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

#FindAreaOfGreenSquare #AreaOfSquare #GeometryMath #MathOlympiad #RightTriangle
#OlympiadMathematicalQuestion #HowToSolveOlympiadQuestion #MathOlympiadQuestion #MathOlympiadQuestions #OlympiadQuestion #Olympiad #AlgebraReview #Algebra #Mathematics #Math #Maths #MathOlympiad #HarvardAdmissionQuestion
#MathOlympiadPreparation #LearntipstosolveOlympiadMathQuestionfast #OlympiadMathematicsCompetition #MathOlympics #CollegeEntranceExam
#blackpenredpen #MathOlympiadTraining #Olympiad Question #GeometrySkills #GeometryFormulas #InscribedCircle #PythagoreanTheorem #SimilarTriangles #CircleTheorem #Tangents
#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
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
Olympiad Question
Geometry
Geometry math
Geometry skills
Right triangles
imo
Competitive Exams
Competitive Exam
Inscribed square
Pythagorean Theorem
Similar triangles
Right Triangle
Square area formula
Triangle area

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

[alster]

Sweet! You made it look easy for me. Kudos from The Philippines 🇵🇭

[santiagoarosam]

Pendiente del lado izquierdo del cuadrado verde: 2/(3-2)=2/1 → Distancia vertical entre vertices verdes superior izquierdo e inferior =1+2+3=6 → Distancia horizontal entre los mismos vértices = 6/2=3 → 6²+3²=36+9=45 =Área cuadrado verde
Gracias y saludos cordiales.

[nineko]

The fact that we don't need the square on the right is an interesting plot twist 😁

[youngbear]

What a smart solution, & a wonderful explanation! Thank you!

[TimBoulette]

The 9 sq unit and 4 sq unit block establish a slope of 2. Height of blocks is 6; therefore base of triangle ABC is 3. From there, it's trivial.

[pwmiles]

By similar triangles the left side of the large square is divided in the ratios 3:2:1, so the middle segment has length s/3. This is the hypotenuse of a right triangle whose other sides are 1 and 2, so

(s/3)^2 = 1^2 + 2^2 = 5
s^2 = 3^2 x 5 = 45

[kennethstevenson]

Great strategy, look for similar right triangles and proportions.

[misterenter-izrz]

Beautiful design of figure, there are 5 similar right angled triangles with lengths ratio 1:2:root 5, so the side of the large square is the hypotenuse of the right angled triangle, square root of 6^2+(0.5+1+1.5)^2=36+9=45, hence the answer is 45, done🙂.

[himo]

√9-√4=3-2=1
1^2+2^2=5 1 : 2 : √5
(√5/2+√5+3√5/2)^2=(3√5)^2=45

[dudiriven]

I calculated the sinus for right triangle created by sides of blue square, yellow square and green square. The angle on the right of this triangle is also at the bottom of the image. If now I consider the big triangle with height of 6, I can apply sinx = 6/s and also sinx = (2√5)/5.
Cross multiply it and we get 30= 2s√5
15=s√5
s=15/√5
s=(15√5)/5
s=3√5
So now I can square it and I get area of green square = s² = 45

[wrecktech]

The only criticism that i have is that while your goal was t to find the area of the square it would have been nice to include the solved side length of 3 SQRT5.

[lk-wryn]

Relation (triangle next the blue square)is 2 to 1, the 3 squares are 6 high so 3 is the base 6^2+3^2=45 is the area of the green square.

[bhavyajindal]

we can also do this problem through similar triangles, taking area of blue square as base.

[vcvartak]

I think no need for the dimension of right square (4 unit)

[alinayfeh]

(4)-√(9)√=1, +3²+(3+2+1)²=45 length of square √(45) after √(45)²=Area green square 🟩 45 units

[vfxgenie]

i did it it differently, the enlargment factor of 2 to 3 was x1.5, and /2 the other way, so you do √5/2+√5+3√5/2)^2=(3√5)^2=45

[cz]

One flaw in the setup: you need to assume the blue square on top of the yellow one, to be exactly positioned on the left side, making the left sides of the yellow square and the blue one as vertical extension of each other. As you said, its visual not on scale and the visual presentation must not used as accurate . Even a small deviation makes a difference to the whole calculation.

Yes, its obvious to assume such ideal positioning between those two squared i named. But in exact science, it leaves some room to differ about this assumption. To be more precise, teachers should include another notion about those two squares to be positioned in relation to each other as clear data, before calculation starts.

Else its not math, but an educated guess

[bigm]

Don’t be afraid of the Big Green Square. It has been subdued by the Professor!🥂