Can you find the area of the Purple shaded region?

No video

Can you find the area of the Purple shaded region? | (Step-by-step explanation) |

Рет қаралды 23,662

Күн бұрын

Learn how to find the area of the Purple shaded region. Important Geometry and algebra skills are also explained: Pythagorean Theorem; area of a parallelogram formula. Step-by-step tutorial by PreMath.com
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!
Step-by-step tutorial by PreMath.com
• Can you find the area ...
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
/ premath
Can you find the area of the Purple shaded region? | (Step-by-step explanation) | #math #maths
Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!
#FindAreaOfPurpleRegion #AreaOfParallelgram #AreaOfTriangle #GeometryMath #MathOlympiad #Triangles #RightTriangles #AreaOfSquare #AreaOfRectangle #PythagoreanTheorem #AreaOfTriangle #IsoscelesTriangle #EquilateralTriangle
#PreMath #PreMath.com #MathOlympics #HowToThinkOutsideTheBox #ThinkOutsideTheBox #HowToThinkOutsideTheBox? #FillInTheBoxes #GeometryMath #Geometry #RightTriangles
#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 #Length #Width
#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
Two Methods to Solve System of Exponential of Equations
Olympiad Question
Find Area of the Shaded Triangle in a Rectangle
Geometry
Geometry math
Geometry skills
Pythagorean Theorem
area of a parallelogram formula
Parallelogram
Square
imo
Competitive Exams
Competitive Exam
Area of a Triangle
Area of a Triangle formula
premath
premaths
Pythagorean Theorem
Similar triangles
Equilateral triangle
Isosceles triangle
coolmath
my maths
mathpapa
mymaths
cymath
sumdog
multiplication
ixl math
deltamath
reflex math
math genie
math way
math for fun
Subscribe Now as the ultimate shots of Math doses are on their way to fill your minds with the knowledge and wisdom once again.

Пікірлер: 71

@bigm383 10 ай бұрын

Thanks Professor.😁📐😃

@PreMath 10 ай бұрын

You are very welcome ❤️ You are awesome. Keep it up 👍

@Waldlaeufer70 10 ай бұрын

long diagonal: d² = 7² + 21² = 49 + 441 = 490 d = √490 = 7√10 short diagonal: e = 7√10 *7/21 e = 7√10 / 3 area of deltoid: A = 1/2 * 7√10 * 7√10/3 A = 1/6 * 49 * 10 A = 490/6 = 245/3 ≈ 81.67 cm²

@PreMath 10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@georgebliss964 10 ай бұрын

Drawing diagonal. Tan of half the parallelogram acute angle = 7/21= 0.333. Tan-1 = 18.435 degrees. Doubling this = 36.87 degrees. In white triangle, tan 36.87 = 7/ base length. Base length = 7/ tan 36.87 = 9.333. Base length of parallelogram = 21 - 9.333 = 11.667. Area = 11.667 x 7. 81.67.

@PreMath 10 ай бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@ybodoN 10 ай бұрын

Generalized: the area of the purple rhombus is _½ (a² + b²) a/b_ where _a_ is the width of the rectangle and _b_ is its length.

@PreMath 10 ай бұрын

Great! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@D.P9 10 ай бұрын

Sir, I think here it should be 1/6 in place of 1/2 Required area = 1/6 (a² + b²)

@ybodoN 10 ай бұрын

@@D.P9 then the formula would only work when the width of the rectangle is one third of its length 🤔

@jimlocke9320 10 ай бұрын

The area of either rectangle is (7)(21) = 147. Using the value of x that PreMath computed, each white triangle has area (1/2)(b)(h) = (1/2)(x)(7) = (1/2)(196/21)(7) = 196/6. There are 2 of these triangles inside either rectangle, combined triangle area equals 196/3. So take the area of either rectangle and deduct the combined area of 2 triangles to get the purple area: 147 - 196/3 = 441/3 - 196/3 = 245/3 cm² or 81.67 cm², as PreMath also found.

@harikatragadda 10 ай бұрын

Draw the diagonal d and if h is its perpendicular bisector from the intersection, then by Similarity, h/(d/2) = 7/21 h = d/6 Purple Area = 2(½*d*h) = d²/6 We know d² = 7² + 21² = 490 Purple Area = 245/3

@PreMath 10 ай бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@marioalb9726 10 ай бұрын

tan α = 7/21 = 1/3 α = 18,435° sin 2α = 7 / b b = 7 / sin 2α b = 11,667 cm Area = b . h Area = 11,667 . 7 Area = 81,667 cm² ( Solved √ )

@PreMath 10 ай бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@ramanivenkata3161 10 ай бұрын

Professor sir, After having found out the value of ' X ' , we could arrive at the area of the shaded portion by simply deducting the area of 2 small triangles on the left and right from area of the rectangle. That is 21x7= 147. 147 - 65.33 = 81.67

@PreMath 10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@MarieAnne. 10 ай бұрын

Or we could have set the hypotenuse of the triangle to x and the longer leg to 21-x instead, and once we found x (35/3) we could simply calculate area of parallelogram as height * base = 7x = 245/3 = 81.67

@quigonkenny 4 ай бұрын

By observation, the four white triangles are all similar by AA similarity. Each, being formed from the corner of a rectangle, is a right triangle, and each shares a vertical angle with the one to its left or right. By the fact that opposite sides of a rectangle are parallel, those two pairs of vertical angles are identical. Investigating the dimensions of the triangles, it can be seen that short leg of each triangle is 7, the short side of the rectangle, and that the long leg and hypotenuse add up to 21, the long side of the rectangle. Let x be the length of the long leg of the triangle: White triangle: 7² + x² = (21-x)² 49 + x² = 441 - 42x + x² 42x = 441 - 49 = 392 x = 392/42 = 28/3 The purple area is equal to one of the rectangles minus two of the triangles. A = hw - 2(bh/2) A = 7(21) - (28/3)7 A = 147 - 196/3 A = 441/3 - 196/3 A = 245/3 ≈ 81.67 cm²

@MathsMadeSimple101 10 ай бұрын

Great puzzle!

@Kelgoran 10 ай бұрын

You need to simplify: x= 196/21 = 28/3 Also, there is an easier way to solve for x: Let: y = hypotenuse of the green triangle We have: (Eq 1) x+y = 21 (Eq 2) 7^2 + x^2 = y^2 (pythagorean theorem) -> (x-y)(x+y)=-7^2 (by Eq 2) x-y = -7^2 / 21 = -7/3 (by Eq 1) x = (21 -7/3)/2 = 28/3 (by Eq 1)

@fikirfikir3039 10 ай бұрын

نحسب القطر الكبير للشكل الأحمر 22.13 نقسم الشكل الأحمر الى أربع مثلثاث..ونحسب زاوية ميل القطر 18.43درجة..ثم نحسب مساحة المثلث الواحد ونضرب بأربعة

@PreMath 10 ай бұрын

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

@fikirfikir3039 10 ай бұрын

@@PreMath Thank you

@yalchingedikgedik8007 10 ай бұрын

Thanks Sir Thanks PreMath That’s nice

@musicsubicandcebu1774 10 ай бұрын

If the sides of a right triangle can be written in the form a, x and b-x, where a and b are known, then x can be found.

@HappyFamilyOnline 10 ай бұрын

Amazing 👍 Thanks for sharing😊

@user-gs4cq3uk2b 10 ай бұрын

(0,0) (21,7) (35/3,0) twice the area of the triangle formed these three points S=|(21,7)x(35/3,0)|=245/3

@PreMath 10 ай бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@EPaozi 10 ай бұрын

On peut aussi utiliser les intégrales !!!

@cyruschang1904 10 ай бұрын

The length of each side of the purple area is x x^2 = 7^2 + (21 - x)^ 2 x^2 = 7^2 + 21^2 - 2(21)x + x^ 2 0 = 7^2 + 21^2 - 2(21)x 2(21)x = 7^2 + 21^2 2(3)x = 7 + 3(21) = 70 3x = 35 x = 35/3 The area of the purple area = 7 (35/3) = 245/3

@misterenter-iz7rz 10 ай бұрын

The other rectangle is made by rotating about the diagonal. Generally the rectangle is a × b, x^2=a^2+(b-x)^2=a^2+b^2+x^2-2bx, x=(a^2+b^2)/2b, the area is a(a^2+b^2)/2b.😊

@gauravroy8528 10 ай бұрын

Hi everyone. Let us consider the largest diagonal of rhombus to be the diagonal of the rectangle given by √(7²+21²)=7√10 which is equal to Smallest side of rectangle ÷ sin θ Hence sinθ = 1/√10 Again the smallest diagonal of rhombus is given by, Smallest side of the rectangle ÷ cos θ Where cosθ = √(1-sin²θ) =3/√10 Therefore the area of rhombus = largest diagonal × 1/2 of smallest diagonal = 7√10 × (1/2) × (7√10)/3 = 490/6= 81.67 square units.

@santiagoarosam430 10 ай бұрын

La zona sombreada o solapo de los dos rectángulos es un rombo cuya superficie es la mitad del producto de sus dos diagonales, D y d → D²=7²+21²=490 → D=√490 →→ El triángulo rectángulo de lados 7/21/D es semejante al de lados b/7/d → Razón de semejanza s=7/21→ d=s*D → Área zona sombreada =D*d/2 =D*s*D/2 =s*D²/2 =(7/21)(√490)²/2 =7*490/21*2=81.6666 Gracias y saludos.

@Copernicusfreud 10 ай бұрын

Yay! I solved the problem.

@PreMath 10 ай бұрын

Bravo❤️ You are awesome. Keep it up 👍

@KAvi_YA666 10 ай бұрын

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

@misterenter-iz7rz 10 ай бұрын

7/x=7/y, so y^2=x^2=(21-x)^2-7^2=21^2-7^2-42x, 0:09 x=(21^2-7^2)/42=28/3, y=21-28/3=35/3, therefore the answer is 35/3x7=245/3.

@PreMath 10 ай бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@education-dd4yi 10 ай бұрын

Thanxs sir ❤❤😊

@PreMath 10 ай бұрын

You are very welcome! You are awesome. Keep it up 👍

@sandrkolesnik 10 ай бұрын

Why you didn't devide 196/21 by 7? => 28/3 Is it simpler to find area 7*21-7*28/3?

@PreMath 10 ай бұрын

Thanks for the feedback. Cheers

@mohanramachandran4550 10 ай бұрын

Thanks. for your service

@PreMath 10 ай бұрын

Thank you too, dear You are awesome. Keep it up 👍

@crazywarxyz911 10 ай бұрын

Can we not congruent both Upper small triangles by ASA criteria as one side and corresponding angles are equal ? Then value of x will 21/2

@PreMath 10 ай бұрын

Many approaches are possible to find the solution to this problem! Cheers

@vrocher93 10 ай бұрын

21*7-7*7/TAN(2*TAN-1(7/21))=81.67 Tangente is always your friend

@PreMath 10 ай бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@krishnashanthi3914 10 ай бұрын

Very good eh

@PreMath 10 ай бұрын

Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@kennethpusingYouTubeChannel 10 ай бұрын

28/3 is the lowest term of 196/21

@luckshmana3461 10 ай бұрын

Nandri sir

@PreMath 10 ай бұрын

மிகவும் வரவேற்கிறோம், அன்பே❤️

@NavSci 10 ай бұрын

Damn nice to see Tamil comments !

@soniamariadasilveira7003 10 ай бұрын

Gostei muito, obrigada

@PreMath 10 ай бұрын

De nada ❤️ Obrigado pelo seu feedback! Saúde! 😀 Você é incrível. Continue assim 👍

@wackojacko3962 10 ай бұрын

@ 4:59 , ...🤔 I know main properties of multiplication of integers as Closure Commutative Associative Distributive Identity and Multiplication by Zero. ...but that "New Math of Criss Cross always throws me for a curve. Cross Multiplication, yes...Criss Cross ...not so much. 🙂 Now the Butterfly Effect, ...that I can relate too. 😉

@PreMath 10 ай бұрын

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