Calculate Perimeter of Trapezoid | Area of Trapezoid is 486 | Trapezium | Important skills explained

[@ix_azeka]

Good problem solving, sir. U are awesome. Love from KZ🇰🇿

[@PreMath]

Glad you think so! Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@mega_mango]

=)

[@moda112]

Happy to say for the first time solved this in a couple minutes by just looking at the thumbnail. Love your geometry quizzes!

[@PreMath]

Great job! Glad to hear that! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@muttleycrew]

Excellent! Congratulations!

[@normanc918]

Thank you for video. Area of trapezoid can be seen as 1.5 of square ABCE, therefore 1.5 a^2 = 486, then a=18, CD = (sq.root 2)(18), perimeter = (4)(18) + (18)(sq.root 2) =(18)(4 + sq.root 2) = (18) (5.414) = 97.46

[@keithwood6459]

I did it this way too. Didn't need to draw anything. Took about a minute.

[@marioalb9726]

Si llamamos side "S" a los lados iguales: Área=486cm² Area= S²+S²/2=3/2 S² S²=486 x 2/3 S= 18 cm Perímetro = 4 S + S/cos45° Perímetro= 97,46 cm. √

[@bangaloresatish6600]

Such an excellent teacher. I am a doctor who learnt this, four decades ago. I still enjoy mathematics and found this channel to be the best. I wish I had him as a teacher and would not have been a doctor. Please keep up the great work, you are a great teacher and inspiration. Please could you do some program on Vedic mathematics, also if possible categorising all the teaching according to the different branches of mathematics and their severity.🙏🏽🙏🏽🙏🏽

[@PreMath]

Wow, thank you! Nice suggestion! So nice of you, Satish You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

[@bangaloresatish6600]

@@PreMath 🙏🏽🙏🏽🙏🏽Mathmatics was always my first and last love but got married to medicine and settled as a paediatrician in UK😀😩 You never get the same satisfaction and joy in medicine like solving these problems. Yes, we do serve people, but that’s human nature and to earn livelihood. Medicine, moreover is not a perfect science. Please 🙏🏽 start working on Vedic mathematics in the same systematic manner you have, so that it becomes available to everyone. Also, please 🙏🏽 compile the video lessons you have already done in various categories, so enthusiasts can access it easily based on their competence. 🙏🏽🙏🏽🙏🏽

[@devondevon4366]

97.456 From the edge of the 45-degree line, draw a perpendicular line to the top of the trapezoid. This line will form an isosceles triangle (45-45-90) and a square since the lines facing the two 45-degree angles are EQUAL. Let the sides of the trapezoid = x and y, with y, the longest side Then the area of the trapezoid is 486 = (( y + x) h)/2 Since x = side of the square and since the triangle to the left is an isosceles, then y=2x and h= x hence 486= [(2x + x )x]/2 972= 3x^2 324 =x^2 18 = x The sides of the trapezoid (excluding the hypotenuse) are : 18, 18, 36 = 72 the hypotenuse can be found by the square root of ( 18^2 + 18^2) or the square root of 648 =25.4558 The perimeter = 72 + 25.4558 = 97.4558 round to 97.456

[@MrPaulc222]

Good stuff, thank you. I started off trying two isosceles right triangles. It might have been possible that way, but then I realised the square + right isosceles would be easier. I got 72 + 18*sqrt(2). I got rid of the fraction by doubling both sides for 3a^2=972. I ignored Pythagora because the diagonal of a square is sroot2. Although I use more shortcuts these days, I have learned many of them from you.

[@jonathanjose6531]

Did the same steps as you did. I paused and tried, got it. Nice problem, thanks for the ideas and time you share. God bless.

[@PreMath]

Excellent! Glad to hear that! Thanks for your feedback! Cheers! You are awesome, Jonathan. Keep it up 👍 Love and prayers from the USA! 😀

[@theoyanto]

Nice simple problem, almost mental arithmetic, a great example to try to approximate in your head because it gives it a reasonable brain workout .. thanks very much 👍🏻

[@HappyFamilyOnline]

Awesome👍 Thanks for sharing😊😊

[@muttleycrew]

Thanks for uploading. Working on these problems is very satisfying. I try to do them without aid of a calculator too which usually means leaving answers as exact values.

[@Ankitsingh-y4j8m]

We learn a lot because of your question sir

[@PreMath]

Excellent! Glad to hear that! Thanks for your continued love and support! You are awesome, Ravi. Keep it up 👍 Love and prayers from the USA! 😀

[@bigm383]

Thanks for an easy but fun problem!❤🥂

[@PreMath]

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

[@bigm383]

@@PreMath 👍😃

[@santiagoarosam430]

AB=a → a²=486x2/3 → a=18 → DC=a√2 → Perímetro ABCD =4a + a√2 =a(4+√2) =18(4+√2) =97.4558 Gracias y saludos cordiales.

[@AmirgabYT2185]

P=72+18√2=18(4+√2)≈97,38 cm

[@otisammathematics9887]

Thank you Sir. I like your videos.

[@mahatmapodge]

The object can be considered as Three 45° isosceles triangles, The square component is 2/3 of the total area, so the side length can be calculated by Sqrt(486 * 2/3) = 18 As the remaining component is a 45° isosceles triangle we know the length of the hypotenuse is Sqrt(2) times the side length Sqrt(2) * 18 = 25.45582 25.46 + (18 *4) = 97.46 cm

[@bramont6225]

Excelente profesor felicidades por el dominio que tiene usted del teorema de Pitágoras y gracias.

[@PreMath]

¡De nada! ¡Gracias por su continuo amor y apoyo! Usted es maravilloso. Sigue así 👍 ¡Amor y oraciones desde los EE. UU.! 😀

[@johnspathonis1078]

A long way round a simple solution. By inspection, the tapezoid is made up of three equal sized triangles of area = 162. Two of these form a square therefore a = sqrt 162 x 2 = 18. Therefore circum is 4 x 18 + 18 x sqrt 2.

[@marioalb9726]

Total Area = 486 cm² Taking 1 of the 3 equals internal right triangles, Area triangle= 486 / 3 = 162 cm² Area triangle = b.h /2 = s²/2=162 s²=2 x 162 s = 18m Perimeter = 18x4 + 18/cos45° Perimeter = 97,46 cm ( Solved √ )

[@georgebliss964]

Area of square = a^2. Area of triangle = 0.5 (a^2) a^2 + 0.5 (a^2) = 486. 1.5 (a^2) =486. a^2 = 486/1.5. a^2 = 324. a =18. Perimeter = 4a + (a x sqrt.2). 72 + (18 x 1.4142) 72 + 25.46. 97.46.

[@alexundre8745]

Good Morning Master Thanks to Sir

[@Copernicusfreud]

Yay! I solved it.

[@PreMath]

Excellent! Glad to hear that! Thanks for sharing! Cheers! You are awesome, Mark. Keep rocking 👍 Love and prayers from the USA! 😀

[@mahalakshmiganapathy6455]

Nice🎉

[@kennethstevenson976]

When I looked at the diagram and found three congruent triangles which gave me the equation 3/2 X^2 = 486. I then found X=18. Since DC^2 = 2 X^2 , I found that DC = 18 root2. Then P = 4x + 18 root 2 , then P = 18 (4 + root 2). P = 18 ( 4 + 1.414 ) , P = 18(5.414). Finally P = 97.452 cm.

[@mohanramachandran4550]

√ ( Area ÷ 1.5 ) = a Perimeter = 4a + a √2 √ ( 486 ÷ 1.5 ) = 18 4 * 18 + 18 √2 = 97.45584

[@PreMath]

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

[@mohanramachandran4550]

Thanks sir

[@jackhusky9326]

There is no need to calculate the areas A1 A2. Because DE is “a” can simply jump straight to trapezoid formula (a+b)/2 * h =486 where a is “a” b is “a+a” and h is “a”. Can then calculate “a” and hence perimeter

[@prithvisinghpanwar007]

i got it 72+sqrt(648) approx. 97.5cm

[@quigonkenny]

Let E be a point on AD where EC is perpendicular to AD. By observation, ECBA is a square with side length s. Also by observation, ∠DCE is 45°, as ∠EDC is also 45° and ∠CED is 90°. This makes ∆CED an isosceles right triangle with base and height of s and hypotenuse of s√2. The perimeter of the trapezoid will thus be (4+√2)s as it encompasses three sides of the square and all but one leg of the triangle. Trapezoid DCBA: A = h(a+b)/2 = s(2s+s)/2 486 = 3s²/2 s² = (2/3)486 = 2(162) = 324 s = √324 = 18 cm P = (4+√2)18 = 72 + 18√2 ≈ 97.46 cm

[@philipkudrna5643]

Before watching: the figure is 1,5 squares, so the area of the solo square is 486/1.5 = 324. So one side is sqrt(324) or 18. The perimeter is 4*18+18*sqrt(2) or 18(4+sqrt(2)) or 97,46.

[@adgf1x]

Let h be the altitude of the trapizoid.then h(h+2h)/2=486=>3h^2 =972=>h^2=972/3=324=18^2 =>h=18unit.perimetsr=18(4+2^0.5) unit.

[@36sidharthghangas32]

join AC = DC = sqrt2*x 3*(area of triangle edc)=area of trapezoid=486{bcz three triangles are congurent} ar=.5*x*x (3/2)*x*x=486 x=18 ;AC =1.414*18

[@miguelgnievesl6882]

The area of a trapezoid is (B+b)h/2 B is the major base, b is the minor base, and h is the height. In this case B=AD, b=BC and h=AB, but AD=2a, BC=a and AB=a. Consequently Area_Trap=(2a+a)a/2. So 3a²/2=486cm². Therefore a=18cm. The perimeter is AB+BC+CD+AD. CD=√2a (by the Pythagorean Theorem). Per=4y+√2y. We substitute "a" and obtain that Per=(72+18√2)cm. or Per≈97.46

[@miguelgnievesl6882]

Correction: It is not 4y+√2y; but 4a+√2a.

[@shadmanhasan4205]

The Trapazoid comes in 2 parts: the square part + the 45+45 isoceles triangle part; let's distribute the area into 2 parts 1st: 486(2/3)[square] + 486(1/3)[triangle] 324cm^2[square] + 162cm^2[triangle] the side-lenghth of the square = Root(324) = 18.0 cm. There is a diagonal with the triangle: 18×(Root(2)) = 25.456 cm -> perimeter = 4(18.0) + 25.456 = 97.456 cm

[@Auberge79]

This time I made it by myself, even easier. As long as CB is equal to BA and AD is perpendicular to AB we simply get one square and a half (by diagonal). So we divide 486 by 3 and get a half square (162), then multiply that by 2 and get the square area (324). This way we can find the side length of the square - the root of 324, which is 18. So we know almost all sides of the perimeter - CB=18, BA=18, AD=2*18 and it only needed to find CD using Pythagorean theorem as square root of (18^2+18^2), square root of 648, which is 25.455844 according to calculator 🙂 Next we count 18*4+25.455844 and the answer is about 97,455844.

[@Auberge79]

I skipped that 45 degrees will result equal sides of the "half square" triangle.

[@alster724]

Super easy

[@vidyadharjoshi5714]

ABsq + 0.5*ABsq = 486. AB = 18. DC = sqrt(2*ABsq) = 25.45. Perimeter = 4*18+25.45 = 97.45

[@ix_azeka]

Easy task, sir

[@PreMath]

Thanks for your feedback! Cheers!

[@pranavamali05]

👍

[@PreMath]

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

[@himo3485]

(2x+x)＊x/2=486 3x^2=972 x^2=324 x=18 36+18+18+18√2=72+18√2(cm)

[@PreMath]

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

[@enessuna99]

3a^2 / 2 = 486 , a^2 = 324 , a= 18 , Calculate Perimeter of Trapezoid = 18 + 18 + 18 + 18 + 648^1/2 =72 + 638^1/2

[@RoderickEtheria]

486×2/3=324 324^1/2=18 18×4+18 sqrt 2=72+18 sqrt 2

[@giuseppemalaguti435]

P=18(4+sqrt2)

[@PreMath]

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

[@SamsungJ-kk5nr]

Parece difícil pero no lo es, solo usando fórmulas .

[@procash1968]

Guru Ji, din't understand how you got 3a²

[@batavuskoga]

Why not solving it as follows ? I think it's much easier. area trapezoid=[(small base+large base)*height]/2 AB=BC=AE=CE=DE - DE is the same langth as CE and BC because the angle at point D is 45° area=[(2a+a)*a]/2=(2a²+a²)2 486=3a²/2 -->486*2=3a² --> a²=324 --> a=18 CD=a*sqrt(2) perimeter=DE+AE+AB+CB+CD=4a+a*sqrt(2)=72+18*sqrt(2)=appr. 97.45 cm

[@bentels5340]

Again, solved it the same way. This time I didn't need a notepad. 😉

[@sachinkhadka8127]

First

[@PreMath]

Excellent! Thank you! Cheers! You are awesome, Sachin. Keep it up 👍 Love and prayers from the USA! 😀

[@ybodoN]

An alternative with the added constraint to only use the given letters ABCD: Draw CA to obtain two right isosceles triangles. This special triangle is known for having the angles in the ratio 1 : 1 : 2 (i.e. 45° - 45° - 90°) and the sides in the ratio 1 : 1 : √2 (which follows immediately from the Pythagorean theorem). Take AB = BC = a so AC = CD = a√2. Similarly, DA = (a√2) √2 = 2a. Therefore, the perimeter of this kind of trapezoid is 4a + a√2 = a (4 + √2). Since triangle ACD is twice as large as triangle ABC, a = √(⅔ 486) = 18 cm. Therefore, the area of this trapezoid is (18 (4 + √2)) cm².

[@thomakondaciu6417]

P=97,452

[@bud2171]

why not divide 486 by 3 ( 3 equal triangles)and find the "a" value which is 18 units that's the rest of the story.