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

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

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[ix_azeka]

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

[marioalb]

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. √

[devondevon]

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

[normanc]

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

[moda]

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

[bangaloresatish]

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.🙏🏽🙏🏽🙏🏽

[jonathanjose]

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.

[MrPaulc]

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.

[mohanramachandran]

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

[Ankitsingh-yjm]

We learn a lot because of your question sir

[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 👍🏻

[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.

[bramont]

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

[misterenter-izrz]

486x2/3=324, sqrt(324)=18 is the side of the square, thus the perimeter is 18x4+18 root(2)=97.456 approximately, done 😊.g

[marioalb]

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 √ )

[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

[georgebliss]

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.

[prithvisinghpanwar]

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

[santiagoarosam]

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.

[johnspathonis]

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.